Trapezoid Rule

Numerical Analysis · Axiom Academy

Approximating integrals by connecting endpoints with straight lines The Trapezoid Rule approximates the area under a curve by connecting the function values at the endpoints with a straight line, creating a trapezoid. The area of a trapezoid is the average of the parallel sides times the height. For integration: Let's approximate the integral of x² from 0 to 1: The error in the single-interval Trapezoid Rule depends on the second derivative: 5. Comparison with Other Methods How does the Trapezoid Rule compare to Riemann sums?

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