Midpoint and Trapezoidal Rules

Approximating Integrals There are some cases when it is impossible to find the definite integral They can be approximated by using types of Riemann sums animations

Midpoint Rule Midpoints of drawn rectangles are used where

Trapezoidal Rule Uses trapezoids instead of rectangles

Example Use both the Midpoint and Trapezoidal rules to evaluate the integral with n = 5

Practice Use both the midpoint and trapezoidal rule to find the integral below for n = 4

Simpson’s Rule Simpson’s Rule uses parabolas rather than rectangles to approximate the integral Numerical Analysis Animations

Example Use Simpson’s Rule to find the integral below for n = 10