Most of the time when we’ve looked at definite integrals, we’ve been used to giving an exact answer by using antiderivatives and the Second Fundamental Theorem. In real life, alas, finding antiderivatives in a useful form can be difficult or impossible. Sometimes the best you can do is find an approximation to the value of your integral. So we’ll look at three techniques for estimating definite integrals: strips, the trapezoidal rule, and Simpson’s rule. In summary, here’s the plan for this final appendix:
• estimating definite integrals using strips, the trapezoidal rule, and Simpson’s rule; and
• estimating the error in the above approximations.