\int _ { - \pi } ^ { \pi } f ( x ) d x ; \quad f ( x ) = \left\{ \begin{array} { l l } { 1 + 2 \cos x , } & { - \pi / 2 \leq x \leq \pi / 3 } \\ { \text{Solve for } g \text{ where} } \\ { \text{Solve for } g \text{ where} } \\ { \text{Solve for } g \text{ where} } \\ { \text{Solve for } g \text{ where} } \\ { \text{Solve for } g \text{ where} } \\ { \text{Solve for } g \text{ where} } \\ { ( 3 / \pi ) r + 1 , } & { \pi / 3 < x \leq \pi } \end{array} \right.