What is trapezoidal approximation?

Trapezoidal approximation involves the use of trapezoids to estimate the area covered by a definite integral. The interval of the curve on the x axis is partitioned into equal partitions that form the bases of trapezoids after which the integral is estimated by adding the areas of all the trapezoids.

The number of trapezoids used determines the accuracy of the approximation since increasing the number of trapezoids increases accuracy, and reducing them diminishes accuracy. Trapezoid approximation can also be obtained by averaging the left and right rectangle approximations for the integral. In most cases, the approximation of the midpoint rectangle sums is twice as good as the trapezoidal approximation.