Chapter 5.3, Problem 51E

Think About It The graph of f consists of line segments and a semicircle, as shown in the figure. Evaluate each definite integral by using geometric formulas.

(a) ${\displaystyle {\int }_0^{2}f\left(x\right)dx}$

(b) ${\displaystyle {\int }_2^{6}f\left(x\right)dx}$

(c) ${\displaystyle {\int }_{-4}^{2}f\left(x\right)dx}$

(d) ${\displaystyle {\int }_{-4}^{6}f\left(x\right)dx}$

(e) ${\displaystyle {\int }_{-4}^6\left|f\left(x\right)\right|dx}$

(f) ${\displaystyle {\int }_{-4}^6\left[f\left(x\right)+2\right]dx}$