Precision Calculation for Integrals and Accumulated Values
Area Under Curve Calculator
Calculate the definite integral of a function within specified bounds to find the area under the curve.
Enter the function of x. Use 'x' as the variable. Supported: +, -, *, /, ^ (power), sin(), cos(), tan(), exp(), log().Please enter a valid function.
The starting point of the integration interval.Please enter a valid number for the lower bound.
The ending point of the integration interval.Please enter a valid number for the upper bound.
Higher number of intervals increases accuracy (e.g., 1000, 10000).Please enter a positive integer for the number of intervals.
Simpson's Rule
Trapezoidal Rule
Choose a numerical integration method. Simpson's Rule is generally more accurate.
Calculation Results
Area Under Curve: –(Definite Integral Value)
Interval Width (Δx): –(Width of each sub-interval)
Number of Iterations: –(Used in numerical approximation)
Integration Method: –(Algorithm applied)
Formula Used: Numerical integration (Simpson's or Trapezoidal Rule) approximates the definite integral ∫ba f(x) dx by summing areas of small shapes (parabolas or trapezoids) under the curve.
Visual Representation
Area under the curve f(x) = – from x = – to x = –
Interval Data
Sample of Function Values within Intervals
Interval Midpoint (xi)
Function Value (f(xi))
Cumulative Area Increment
Enter inputs and click 'Calculate Area' to see data.
What is Area Under Curve?
{primary_keyword} is a fundamental concept in calculus and applied mathematics that quantifies the accumulated value of a function over a specified interval. Essentially, it represents the exact geometric area bounded by the function's curve, the x-axis, and two vertical lines corresponding to the interval's start and end points. In practical terms, the area under a curve can represent various cumulative quantities depending on the function's meaning. For example, if f(t) represents velocity over time, the area under the curve from t=a to t=b gives the total displacement during that time interval. If f(t) represents a rate of flow, the area gives the total volume or quantity that has passed. Understanding {primary_keyword} is crucial in fields like physics, engineering, economics, statistics, and computer science for analyzing rates of change and calculating total quantities.
Who should use it? Anyone dealing with continuous functions and needing to calculate accumulated quantities, such as engineers determining total work done, physicists calculating distance from velocity, economists analyzing cumulative profit, or data scientists estimating probabilities from probability density functions. It's a core concept for students in calculus and related STEM fields.
Common Misconceptions: A frequent misunderstanding is that "area under the curve" always refers to a positive value. However, if the function dips below the x-axis within the interval, the definite integral (and thus the calculated area) will be negative for that portion, effectively subtracting from the total accumulated value. Another misconception is confusing the concept with simple geometric shapes; while simple shapes can be integrated directly, calculus provides the tools for complex, non-linear curves. Lastly, people sometimes confuse the geometric area with the *net signed area*, where areas below the x-axis are treated as negative contributions.
Area Under Curve Formula and Mathematical Explanation
The precise mathematical tool for finding the {primary_keyword} is the **definite integral**. For a continuous function f(x), the definite integral from a lower bound 'a' to an upper bound 'b' is denoted as:
∫ab f(x) dx
This notation asks for the accumulated value of f(x) as x ranges from a to b.
Derivation via Riemann Sums (Conceptual):
While the fundamental theorem of calculus provides the most efficient way to evaluate definite integrals (if an antiderivative F(x) is known, the integral is F(b) – F(a)), understanding the concept often starts with Riemann sums. This involves:
Partitioning the Interval: Divide the interval [a, b] into 'n' smaller sub-intervals, each of width Δx = (b – a) / n.
Choosing Sample Points: Select a representative point (xi*) within each sub-interval [xi-1, xi]. Common choices include the left endpoint, right endpoint, or midpoint.
Forming Rectangles/Shapes: Construct rectangles (or trapezoids, or parabolic segments) whose height is determined by the function's value at the sample point, f(xi*), and whose width is Δx.
Summing Areas: Calculate the area of each shape (e.g., height × width for rectangles) and sum them up: Σi=1n f(xi*) Δx.
Taking the Limit: As the number of intervals 'n' approaches infinity (and Δx approaches zero), this sum converges to the exact area under the curve.
Numerical Integration Methods: Since finding the exact antiderivative isn't always possible, we use numerical methods to approximate the integral:
Trapezoidal Rule: Approximates the area within each sub-interval using a trapezoid. The formula is Δx/2 * [f(x0) + 2f(x1) + … + 2f(xn-1) + f(xn)].
Simpson's Rule: Approximates the area using parabolic segments, generally providing higher accuracy for the same number of intervals. The formula requires an even number of intervals and is Δx/3 * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + … + 2f(xn-2) + 4f(xn-1) + f(xn)].
Variables in Area Under Curve Calculation
Variable
Meaning
Unit
Typical Range
f(x)
The function defining the curve
Depends on context (e.g., m/s, units/hr)
Varies widely
a
Lower bound of integration
Units of x (e.g., seconds, meters)
Real number
b
Upper bound of integration
Units of x (e.g., seconds, meters)
Real number
Δx
Width of each sub-interval
Units of x
Positive, small value (e.g., 0.001)
n
Number of sub-intervals
Count
Positive integer (e.g., 100, 10000)
Area
Calculated area under the curve
Units of f(x) * Units of x (e.g., meters, kg*m)
Real number (can be negative)
Practical Examples (Real-World Use Cases)
Example 1: Calculating Distance Traveled
A car's velocity is given by the function v(t) = 3t2 + 2t m/s, where 't' is time in seconds. We want to find the total distance traveled from t = 1 second to t = 5 seconds.
Function: f(t) = 3t2 + 2t
Lower Bound (a): 1
Upper Bound (b): 5
Number of Intervals (n): 10000 (for high accuracy)
Method: Simpson's Rule
Calculation: Using the calculator with these inputs, we find the area under the velocity-time curve.
Result: The calculator might yield an area of approximately 136.00 units.
Interpretation: The area under the velocity-time curve represents the displacement. Therefore, the car traveled 136 meters between t=1 and t=5 seconds. This is a direct application of {primary_keyword} in kinematics.
Example 2: Estimating Cumulative Profit
A startup's marginal profit function (rate of profit increase) is approximated by P'(x) = -0.5x2 + 10x + 50 dollars per unit sold, where 'x' is the number of units sold. We want to estimate the total profit generated from selling the first 10 units.
Function: f(x) = -0.5x2 + 10x + 50
Lower Bound (a): 0
Upper Bound (b): 10
Number of Intervals (n): 5000
Method: Trapezoidal Rule
Calculation: Inputting these values into the area under the curve calculator.
Result: The calculator might show an area of approximately 750.00 units.
Interpretation: The area under the marginal profit curve from 0 to 10 units sold represents the total profit accumulated over that range. The startup's total profit from selling the first 10 units is approximately $750. This helps in understanding revenue generation and marginal analysis, a key aspect of financial modeling.
How to Use This Area Under Curve Calculator
Enter the Function: In the "Function f(x)" field, type the mathematical expression for your curve. Use 'x' as the independent variable. You can use standard operators (+, -, *, /), powers (^), and common functions like sin(), cos(), exp(), log(). For example: `2*x^3 – sin(x) + 5`.
Define the Interval: Specify the "Lower Bound (a)" and "Upper Bound (b)" for your calculation. This is the range over which you want to find the area.
Set Accuracy: Input the "Number of Intervals (n)". A larger number generally yields a more accurate result but takes slightly longer to compute. 1000 is a good starting point; 10000 or more provides high precision.
Choose Method: Select your preferred "Integration Method". Simpson's Rule typically offers better accuracy than the Trapezoidal Rule for the same 'n'.
Calculate: Click the "Calculate Area" button.
Reading the Results:
Area Under Curve: This is your primary result, representing the definite integral value or accumulated quantity.
Interval Width (Δx): Shows the size of each segment used in the approximation.
Number of Iterations: Confirms the 'n' value used.
Integration Method: Indicates which algorithm was applied.
Decision-Making Guidance: The calculated area provides crucial insights. For instance, in physics, a positive area under a force-displacement graph indicates work done *by* the force. A negative area might signify work done *against* the force. In finance, positive area under a profit-rate curve implies cumulative profit, while negative area suggests cumulative loss. Always interpret the area in the context of the function and its units.
Key Factors That Affect Area Under Curve Results
While the core calculation involves the function and interval, several factors influence the interpretation and practical application of {primary_keyword}:
Function Complexity: Non-linear functions or those with discontinuities (jumps, asymptotes) within the interval can be challenging for numerical methods. Higher 'n' might be needed, or the function might need piecewise integration. This impacts the accuracy of the integral approximation.
Interval Width (b – a): A larger interval means more accumulated value is being measured. If the function's rate of change is high over a large interval, the total accumulated quantity can be substantial.
Number of Intervals (n): Directly impacts accuracy. Too few intervals lead to significant under/overestimation (error). Increasing 'n' refines the approximation, especially for rapidly changing functions. This is a key aspect of numerical analysis.
Choice of Integration Method: Simpson's Rule generally converges faster (requires smaller 'n' for the same accuracy) than the Trapezoidal Rule because it uses parabolic segments, which better approximate curves than straight lines.
Units of Measurement: The units of the resulting area are the product of the units of the function's output (y-axis) and the units of the independent variable (x-axis). Misinterpreting units (e.g., meters/second * seconds = meters) can lead to incorrect conclusions.
Sign of the Function: Portions of the curve below the x-axis (f(x) < 0) contribute negative area. The calculated definite integral is the *net signed area*. If only the geometric area is desired, one must integrate the absolute value of the function, |f(x)|, or split the interval at the x-intercepts. This is critical in applications like calculating net change versus total change.
Computational Precision: While the calculator aims for high accuracy, extremely large 'n' or very complex functions can sometimes lead to floating-point errors in computation. This is a minor concern for most practical uses but relevant in high-performance computing.
Real-world Modeling Accuracy: The function f(x) itself is often a model or approximation of a real-world phenomenon. The accuracy of the {primary_keyword} result is fundamentally limited by how well the function represents reality. Factors like economic forecasting models or physical process simplifications play a role.
Frequently Asked Questions (FAQ)
Q1: What is the difference between a definite integral and an indefinite integral?
A1: An indefinite integral (antiderivative) results in a function F(x) + C, representing a family of functions whose derivative is f(x). A definite integral, calculated over an interval [a, b], results in a single numerical value representing the net signed area under the curve f(x) between a and b.
Q2: Why does the calculator ask for the number of intervals (n)?
A2: Most functions cannot be integrated analytically (finding an exact antiderivative). Numerical methods approximate the integral by dividing the area into many small shapes (like trapezoids or parabolic segments). 'n' determines how many such shapes are used; a higher 'n' leads to a more accurate approximation of the true area.
Q3: Is Simpson's Rule always better than the Trapezoidal Rule?
A3: Simpson's Rule is generally more accurate for smooth functions because it approximates the curve using parabolas, which follow curves better than the straight lines used by the Trapezoidal Rule. However, the Trapezoidal Rule is simpler and can be more efficient for functions where higher-order polynomials don't fit well or for specific error analysis.
Q4: What happens if my function goes below the x-axis?
A4: The definite integral calculates the "net signed area." Portions of the curve below the x-axis contribute negative values to the total sum. If you need the total geometric area (always positive), you would need to integrate the absolute value of the function, |f(x)|, potentially splitting the integral at points where f(x) crosses the x-axis.
Q5: Can this calculator handle complex functions like integrals with logarithms or trigonometric functions?
A5: Yes, the underlying JavaScript math functions can handle standard mathematical operations, powers, and built-in trigonometric (sin, cos, tan) and logarithmic (log, exp) functions. Ensure you use the correct syntax (e.g., `sin(x)`, `log(x)`).
Q6: What are the units of the result?
A6: The units of the area under the curve are the product of the units of the function's output (y-axis) and the units of the independent variable (x-axis). For example, if velocity (m/s) is plotted against time (s), the area is in meters (m). If profit rate ($/unit) is plotted against units sold, the area is in dollars ($).
Q7: How accurate is the result? Can it be 100% correct?
A7: Numerical methods provide approximations. The accuracy increases with the number of intervals (n) and the suitability of the chosen method (e.g., Simpson's Rule). For most practical purposes, a large 'n' (like 10,000+) gives highly accurate results. Exact analytical solutions are only possible for functions with known antiderivatives.
Q8: What is the role of data analysis when calculating area under the curve?
A8: In data analysis, the function f(x) might be a curve fitted to data points. Calculating the area under this fitted curve helps estimate total quantities or cumulative effects from discrete data, providing insights beyond individual data points. It's a way to infer continuous behavior from sampled observations.
Rate of Change CalculatorCalculate derivatives to understand the instantaneous rate of change of functions.
Statistical Probability CalculatorsEstimate probabilities using various distributions, often involving calculating areas under probability density functions.
Understanding Exponential GrowthLearn how exponential functions model rapid increases and their implications in finance and science.
// — Helper Functions —
function evaluateFunction(funcStr, x) {
try {
// Basic sanitization and replacement
funcStr = funcStr.replace(/sin/g, 'Math.sin');
funcStr = funcStr.replace(/cos/g, 'Math.cos');
funcStr = funcStr.replace(/tan/g, 'Math.tan');
funcStr = funcStr.replace(/exp/g, 'Math.exp');
funcStr = funcStr.replace(/log/g, 'Math.log'); // Natural log
// Handle x^n for any n, including decimals
funcStr = funcStr.replace(/x\^(\-?\d+(\.\d+)?)/g, 'Math.pow(x, $1)');
funcStr = funcStr.replace(/x\^x/g, 'Math.pow(x, x)'); // Specific case x^x
funcStr = funcStr.replace(/(\d+(\.\d+)?)\^x/g, 'Math.pow($1, x)'); // Constant^x
funcStr = funcStr.replace(/x\^(\d+(\.\d+)?)/g, 'Math.pow(x, $2)'); // x^constant
// Secure evaluation using Function constructor (safer than eval)
var func = new Function('x', 'Math', 'return ' + funcStr);
return func(x, Math);
} catch (e) {
console.error("Error evaluating function:", e);
return NaN; // Return NaN on error
}
}
function getFloatValue(id, min, max, allowNegative) {
var element = document.getElementById(id);
var value = parseFloat(element.value);
var errorElement = document.getElementById(id + "Error");
if (isNaN(value)) {
errorElement.style.display = 'block';
errorElement.textContent = "Please enter a valid number.";
return null;
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if (!allowNegative && value < 0) {
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if (min !== null && value max) {
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errorElement.textContent = "Value cannot exceed " + max + ".";
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function getIntValue(id, min) {
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var errorElement = document.getElementById(id + "Error");
if (isNaN(value) || value < min) {
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function clearErrors() {
var errorElements = document.querySelectorAll('.error-message');
for (var i = 0; i < errorElements.length; i++) {
errorElements[i].style.display = 'none';
}
}
// — Calculator Logic —
var areaChartInstance = null;
var chartCanvas = document.getElementById('areaChart').getContext('2d');
function calculateArea() {
clearErrors();
var funcStr = document.getElementById('functionInput').value;
var a = getFloatValue('lowerBound', null, null, false); // Can be negative, but often non-negative
var b = getFloatValue('upperBound', null, null, false);
var n = getIntValue('numIntervals', 1);
var method = document.getElementById('integrationMethod').value;
// Specific validation for bounds: b must be greater than a
if (a !== null && b !== null && b <= a) {
document.getElementById('upperBoundError').style.display = 'block';
document.getElementById('upperBoundError').textContent = "Upper bound must be greater than the lower bound.";
a = null; // Invalidate inputs to prevent calculation
}
if (a === null || b === null || n === null) {
// Errors already displayed by getFloatValue/getIntValue
return;
}
var deltaX = (b – a) / n;
var totalArea = 0;
var yValues = [];
var xValues = [];
var cumulativeArea = [];
var currentCumulativeArea = 0;
// Store function name for chart caption
document.getElementById('chartFuncName').textContent = funcStr;
document.getElementById('chartLowerBound').textContent = a;
document.getElementById('chartUpperBound').textContent = b;
// Populate table and calculate intermediate values
var tableBody = document.getElementById('tableBody');
tableBody.innerHTML = ''; // Clear previous table data
if (method === 'simpson') {
if (n % 2 !== 0) {
// Simpson's rule requires an even number of intervals
n++; // Increment n to make it even
deltaX = (b – a) / n;
document.getElementById('numIntervals').value = n; // Update input field
document.getElementById('numIntervalsError').textContent = "Number of intervals adjusted to be even for Simpson's Rule.";
document.getElementById('numIntervalsError').style.display = 'block';
}
// Add endpoints for Simpson's rule calculation
var x0 = a;
var y0 = evaluateFunction(funcStr, x0);
if (isNaN(y0)) { alert("Error evaluating function at x=" + x0); return; }
xValues.push(x0);
yValues.push(y0);
cumulativeArea.push(0); // First cumulative area is 0
totalArea += y0; // Start with the first term
for (var i = 1; i < n; i++) {
var x_i = a + i * deltaX;
var y_i = evaluateFunction(funcStr, x_i);
if (isNaN(y_i)) { alert("Error evaluating function at x=" + x_i); return; }
xValues.push(x_i);
yValues.push(y_i);
if (i % 2 !== 0) { // Odd index
totalArea += 4 * y_i;
} else { // Even index
totalArea += 2 * y_i;
}
// Store intermediate cumulative area for table/chart
currentCumulativeArea += y_i * deltaX; // Approximate increment
cumulativeArea.push(currentCumulativeArea);
}
// Add the last endpoint
var xn = b;
var yn = evaluateFunction(funcStr, xn);
if (isNaN(yn)) { alert("Error evaluating function at x=" + xn); return; }
xValues.push(xn);
yValues.push(yn);
cumulativeArea.push(currentCumulativeArea + yn * deltaX); // Final cumulative area
totalArea += yn; // Add the last term
totalArea *= (deltaX / 3);
} else { // Trapezoidal Rule
// Add endpoints for Trapezoidal rule calculation
var x0 = a;
var y0 = evaluateFunction(funcStr, x0);
if (isNaN(y0)) { alert("Error evaluating function at x=" + x0); return; }
xValues.push(x0);
yValues.push(y0);
cumulativeArea.push(0);
totalArea += y0 / 2.0; // Start with half the first term
for (var i = 1; i < n; i++) {
var x_i = a + i * deltaX;
var y_i = evaluateFunction(funcStr, x_i);
if (isNaN(y_i)) { alert("Error evaluating function at x=" + x_i); return; }
xValues.push(x_i);
yValues.push(y_i);
totalArea += y_i; // Add the middle terms
// Store intermediate cumulative area for table/chart
currentCumulativeArea += y_i * deltaX; // Approximate increment
cumulativeArea.push(currentCumulativeArea);
}
// Add the last endpoint
var xn = b;
var yn = evaluateFunction(funcStr, xn);
if (isNaN(yn)) { alert("Error evaluating function at x=" + xn); return; }
xValues.push(xn);
yValues.push(yn);
cumulativeArea.push(currentCumulativeArea + yn * deltaX); // Final cumulative area
totalArea += yn / 2.0; // Add half the last term
totalArea *= deltaX;
}
// Update results display
document.getElementById('mainResult').textContent = totalArea.toFixed(6);
document.getElementById('deltaX').textContent = deltaX.toFixed(6);
document.getElementById('iterations').textContent = n;
document.getElementById('methodUsed').textContent = (method === 'simpson') ? 'Simpson\'s Rule' : 'Trapezoidal Rule';
// Populate Table (showing first 10 and last 5 rows for brevity)
var maxRowsToShow = 10;
for (var i = 0; i < xValues.length; i++) {
if (i = xValues.length – 5) {
var row = tableBody.insertRow();
var cell1 = row.insertCell(0);
var cell2 = row.insertCell(1);
var cell3 = row.insertCell(2);
cell1.textContent = xValues[i].toFixed(4);
cell2.textContent = yValues[i].toFixed(4);
// Cumulative area calculation needs refinement for accurate display
// For simplicity, let's recalculate based on actual computed sum up to this point
var tempAreaSum = 0;
if (method === 'simpson') {
// Simpson's rule calculation for cumulative increments is complex to display simply.
// We'll show the value at the point, not the cumulative increment easily.
// A simpler approach for the table is showing f(x_i) and the running sum approximation.
cell3.textContent = (i === 0 ? 0 : (cumulativeArea[i] – cumulativeArea[i-1]) ).toFixed(6); // Rough increment
} else { // Trapezoidal
cell3.textContent = (i === 0 ? 0 : (cumulativeArea[i] – cumulativeArea[i-1]) ).toFixed(6); // Rough increment
}
// Adjusting cell3 to show the intermediate sum, not just increment for clarity
if (i > 0) {
cell3.textContent = cumulativeArea[i].toFixed(6);
} else {
cell3.textContent = "0.000000";
}
if (i === maxRowsToShow – 1 && xValues.length > maxRowsToShow + 5) {
var ellipsisRow = tableBody.insertRow();
ellipsisRow.insertCell(0).colSpan = 3;
ellipsisRow.cells[0].textContent = "…";
ellipsisRow.cells[0].style.textAlign = "center";
ellipsisRow.cells[0].style.fontStyle = "italic";
}
}
}
// Update Chart
updateChart(xValues, yValues, totalArea, deltaX, a, b, method);
}
function updateChart(xData, yData, area, dx, lower, upper, method) {
if (areaChartInstance) {
areaChartInstance.destroy();
}
var chartData = {
labels: xData.map(function(x) { return x.toFixed(2); }), // Labels for x-axis ticks
datasets: [
{
label: 'f(x) Function Values',
data: yData,
borderColor: 'rgb(75, 192, 192)',
backgroundColor: 'rgba(75, 192, 192, 0.2)',
fill: false, // Don't fill under the function line itself
tension: 0.1,
pointRadius: 0 // Hide points for the function line for clarity
},
{
label: 'Area Segments (Approximation)',
data: yData.map(function(y, index) {
// This dataset is tricky for showing the *area*.
// We'll use it to visualize the curve itself, and shading indicates area.
// A better approach might involve drawing polygons, but for simplicity:
// We'll just plot the function again, and rely on background shading logic if possible.
// For a pure canvas approach without complex polygon drawing:
// Let's create points that help visualize segments.
// For Simpson's, it's parabolic segments; Trapezoidal is trapezoids.
// A simplified visualization: draw the function line and shade below it.
return y; // Re-plot the function data
}),
borderColor: 'rgba(0,0,0,0)', // Make line invisible
backgroundColor: 'rgba(0, 74, 153, 0.3)', // Shading color for area
fill: 'origin', // Fill from origin (x-axis)
tension: 0.1,
pointRadius: 0
}
]
};
// Adjust fill behavior based on method for conceptual clarity
if (method === 'simpson') {
// Simpson's rule shades areas bounded by parabolas, harder to draw directly.
// We'll stick with the general fill.
} else { // Trapezoidal
// Can conceptually think of filling trapezoids.
}
areaChartInstance = new Chart(chartCanvas, {
type: 'line',
data: chartData,
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
x: {
title: { display: true, text: 'x value' },
min: lower,
max: upper,
ticks: {
autoSkip: true,
maxTicksLimit: 10
}
},
y: {
title: { display: true, text: 'f(x) value' },
beginAtZero: true // Often helpful, but depends on function
}
},
plugins: {
tooltip: {
callbacks: {
label: function(context) {
var label = context.dataset.label || ";
if (label) {
label += ': ';
}
if (context.parsed.y !== null) {
label += context.parsed.y.toFixed(4);
}
return label;
}
}
},
legend: {
display: false // Hide legend, use caption instead
}
},
annotation: {
annotations: [
{
type: 'line',
mode: 'vertical',
scaleID: 'x',
value: lower,
borderColor: 'var(–primary-color)',
borderWidth: 2,
label: {
content: 'Lower Bound (a)',
enabled: true,
position: 'start',
backgroundColor: 'rgba(0, 74, 153, 0.7)',
color: 'white'
}
},
{
type: 'line',
mode: 'vertical',
scaleID: 'x',
value: upper,
borderColor: 'var(–primary-color)',
borderWidth: 2,
label: {
content: 'Upper Bound (b)',
enabled: true,
position: 'end',
backgroundColor: 'rgba(0, 74, 153, 0.7)',
color: 'white'
}
}
]
}
}
});
}
// — Event Listeners & Initialization —
function resetCalculator() {
document.getElementById('functionInput').value = 'x^2';
document.getElementById('lowerBound').value = '0';
document.getElementById('upperBound').value = '1';
document.getElementById('numIntervals').value = '1000';
document.getElementById('integrationMethod').value = 'simpson';
document.getElementById('mainResult').textContent = '-';
document.getElementById('deltaX').textContent = '-';
document.getElementById('iterations').textContent = '-';
document.getElementById('methodUsed').textContent = '-';
document.getElementById('tableBody').innerHTML = '
Enter inputs and click \'Calculate Area\' to see data.
';
clearErrors();
// Clear chart
if (areaChartInstance) {
areaChartInstance.destroy();
areaChartInstance = null;
}
document.getElementById('chartCanvas').getContext('2d').clearRect(0, 0, document.getElementById('chartCanvas').width, document.getElementById('chartCanvas').height);
document.getElementById('chartCaption').innerHTML = 'Area under the curve f(x) = – from x = – to x = -';
}
function copyResults() {
var mainResult = document.getElementById('mainResult').textContent;
var deltaX = document.getElementById('deltaX').textContent;
var iterations = document.getElementById('iterations').textContent;
var methodUsed = document.getElementById('methodUsed').textContent;
var funcInput = document.getElementById('functionInput').value;
var lowerBoundInput = document.getElementById('lowerBound').value;
var upperBoundInput = document.getElementById('upperBound').value;
var copyText = "Area Under Curve Calculation Results:\n\n";
copyText += "Function: " + funcInput + "\n";
copyText += "Interval: [" + lowerBoundInput + ", " + upperBoundInput + "]\n";
copyText += "Method: " + methodUsed + "\n";
copyText += "Number of Intervals: " + iterations + "\n\n";
copyText += "—————————————-\n";
copyText += "Main Result:\n";
copyText += "Area Under Curve: " + mainResult + "\n";
copyText += "Interval Width (Δx): " + deltaX + "\n";
copyText += "—————————————-\n\n";
copyText += "Key Assumptions:\n";
copyText += "- Numerical integration method used.\n";
copyText += "- Accuracy depends on the number of intervals.\n";
var textArea = document.createElement("textarea");
textArea.value = copyText;
textArea.style.position = "fixed";
textArea.style.left = "-9999px";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'Results copied to clipboard!' : 'Copying failed!';
console.log(msg);
// Optionally show a temporary success message to the user
var tempMessage = document.createElement('div');
tempMessage.textContent = msg;
tempMessage.style.position = 'fixed';
tempMessage.style.bottom = '20px';
tempMessage.style.left = '50%';
tempMessage.style.transform = 'translateX(-50%)';
tempMessage.style.backgroundColor = (successful ? 'green' : 'red');
tempMessage.style.color = 'white';
tempMessage.style.padding = '10px 20px';
tempMessage.style.borderRadius = '5px';
tempMessage.style.zIndex = '1000';
document.body.appendChild(tempMessage);
setTimeout(function() {
document.body.removeChild(tempMessage);
}, 3000);
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
}
document.body.removeChild(textArea);
}
// Initialize the calculator on load
document.addEventListener('DOMContentLoaded', function() {
// Add Chart.js library dynamically
var script = document.createElement('script');
script.src = 'https://cdn.jsdelivr.net/npm/chart.js@3.7.0/dist/chart.min.js'; // Use a specific version
script.onload = function() {
// Chart.js loaded, now try to add chartjs-plugin-annotation
var annotationScript = document.createElement('script');
annotationScript.src = 'https://cdn.jsdelivr.net/npm/chartjs-plugin-annotation@1.2.0'; // Use a specific version
annotationScript.onload = function() {
console.log("Chart.js and Annotation plugin loaded.");
// Optionally run calculateArea() here if you want default calculation on load
// calculateArea();
};
annotationScript.onerror = function() {
console.error("Failed to load Chart.js Annotation plugin.");
};
document.head.appendChild(annotationScript);
};
script.onerror = function() {
console.error("Failed to load Chart.js library.");
};
document.head.appendChild(script);
// Add event listeners for real-time updates (optional, but good practice)
var inputFields = document.querySelectorAll('.loan-calc-container input, .loan-calc-container select');
for (var i = 0; i < inputFields.length; i++) {
inputFields[i].addEventListener('input', function() {
// Debounce or throttle if performance is an issue, but for now:
// calculateArea();
});
}
// Trigger initial calculation if default values should be displayed
// calculateArea();
});