The trapezoidal rule is a numerical method used to approximate the definite integral of a function. This calculator allows you to input the lower and upper limits of integration, the number of subintervals, and the function itself to compute the integral using the trapezoidal rule.

Trapezoidal Rule Formula

The trapezoidal rule approximates the integral of a function by dividing the area under the curve into trapezoids rather than rectangles. The formula for the trapezoidal rule is:

∫(a to b) f(x) dx ≈ (h/2) * [f(a) + 2 * Σ f(x_i) + f(b)]

Variables:

  • h = (b - a) / n, the width of each subinterval
  • Σ f(x_i) is the sum of the function values at each subinterval
  • f(a) and f(b) are the function values at the lower and upper limits of integration

To apply the trapezoidal rule, follow these steps:

  1. Divide the interval [a, b] into n