# Chapter 25: Numerical Integration

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## Introduction

We can easily set up a spreadsheet to evaluate a given integrand f at a large number of points in the range from a to b, and to form Riemann sums. A symmetric way to do this is the "trapezoid rule" that approximates the area in a strip by the area in the trapezoid with the same height at either end of the given interval. We explore this rule and more accurate extrapolations. The first of these is called Simpson's rule.

## Topics

25.1 The Trapezoid Rule

25.2 Simpson's Rule

25.3 Extrapolations and Better Approximations

25.4 Numerical Evaluation of Line Integrals

25.5 Doing Flux (Surface) Integrals on a Spreadsheet