Lesson 7.7- Numerical Integration; Simpson’s Rule

If it is necessary to evaluate a definite integral of a function for which an antiderivative cannot be found, then one must settle for some kinds of numerical approximation of the integral.

In (Lesson 5.4) we considered three such approximations in the context of areas:

  • Left endpoint approximation
  • Right endpoint approximation
  • Midpoint approximation.

In this lesson we will extend those methods to general definite integrals, and we will develop some new methods that often provide more accuracy with less computation. We will also discuss the errors that arise in integral approximations.