MAC 2312

The last chapter emphasized a geometric interpretation of definite integrals as "areas" in two dimensions. This section emphasizes another geometrical use of integration, calculating volumes of solid three– dimensional objects such as those shown in Fig. 1. Our basic approach is to cut the whole solid into thin "slices" whose volumes can be approximated, add the volumes of these "slices" together (a Riemann sum), and finally obtain an exact answer by taking a limit of the sums to ...