Trapezoidal Rule Calculator
Approximate the definite integral of any function over [a, b] using the composite trapezoidal rule with n subintervals.
Use the Trapezoidal Rule Calculator
Inputs
Supports: +, -, *, /, ^, sin, cos, tan, exp, log, ln, sqrt, abs, pi, e
Result
Formula Applied
Partition Table
| i | xi | f(xi) | Weight |
|---|
Enter values above and click Calculate to see the approximation.
Summary
The Trapezoidal Rule Calculator approximates the definite integral of a function over a closed interval [a, b] by dividing the interval into n equal subintervals and summing the areas of the trapezoids formed under the curve. It evaluates the function at each partition point and applies the composite trapezoidal formula: h/2 * [f(x0) + 2f(x1) + ... + 2f(x_{n-1}) + f(xn)], where h = (b-a)/n. This numerical integration method is straightforward and useful when an exact antiderivative is difficult or impossible to find.
How it works
- Enter a mathematical function such as x^2, sin(x), or e^x in the function field.
- Set the lower bound a and upper bound b for the integration interval.
- Choose the number of subintervals n (higher values give more accurate results).
- Click Calculate to apply the composite trapezoidal rule formula.
- Review the approximation result along with the step-size h and the partition table.
Use cases
- Estimate areas under curves when an exact integral is hard to compute analytically.
- Verify hand-calculated numerical integration homework answers.
- Explore how increasing n reduces approximation error.
- Integrate empirical data functions in physics and engineering problems.
- Teach or learn the composite trapezoidal method step by step.
- Quick numerical check before applying more complex methods like Simpson's rule.