Area Under Curve Calculator
Enter any math function and interval to instantly compute the definite integral using Simpson's rule numerical integration.
Function & Interval
Use x as variable. Operators: +, -, *, /, ^ or **. Functions: sin, cos, tan, sqrt, exp, log, abs.
Quick Examples
Enter a function and click Calculate to see the result.
Integration Result
∫ f(x) dx
Function
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Interval
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Subintervals
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Method
Simpson's Rule
About Simpson's Rule
Simpson's rule approximates the integral by dividing [a, b] into n equal subintervals and fitting parabolas over each pair. Formula: (h/3)[f(x₀) + 4f(x₁) + 2f(x₂) + ... + 4f(xₙ₋₁) + f(xₙ)] where h = (b-a)/n.
Summary
Enter any math function and interval to instantly compute the definite integral using Simpson's rule numerical integration.
How it works
- Enter a mathematical function in the f(x) field (e.g. x^2, sin(x), e^x).
- Set the lower bound (a) and upper bound (b) of the integration interval.
- Choose the number of subintervals (higher = more accurate).
- Click "Calculate" to run Simpson's rule numerical integration.
- The result displays the approximate area and a summary of the method used.
Use cases
- Estimate the area under a velocity-time graph to find displacement.
- Approximate definite integrals for functions without closed-form antiderivatives.
- Verify calculus homework answers with a quick numerical check.
- Compute areas for irregular curves in engineering design.
- Analyze probability distributions by integrating PDF functions.
- Explore the effect of changing interval bounds on total area.