Chapter 5.2, Problem 32E

Net area and definite integrals Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand, show the region in question, and interpret your result.

32. ${\displaystyle {\int }_1^{10}g(x)dx}$, where $g(x)=\{\begin{array}{ll}4x\hfill & \text{if}0\le x\le 2\hfill \\ -8x+16\hfill & \text{if}2<x\le 3\hfill \\ -8\hfill & \text{if}x>3\hfill \end{array}$