Let f be a continuous function whose domain includes the closed interval [a, b]. We now investigate ways of approximating the definite integral

This will be useful when we cannot find an elementary antiderivative for f or if the function is defined using data obtained from some experiment. Let's use the notation introduced in the summary on Riemann Sums where we discussed three specific approximations of a definite integral:

  1. Riemann sums using left-hand endpoints

  2. Riemann sums using right-hand endpoints

  3. Riemann sums using midpoints.

Trapezoidal Rule:

Simpson's Rule:

Error Bounds.

TI-85 graphing calculator programs for numerical approximation of integrals.