Answer
(a) $$\frac{4}{\pi}$$
(b) $$c = c_1 \approx1.238 or c_2 \approx2.808$$
Work Step by Step
(a) $$f_{ave} = \frac{1}{\pi} \int^{\pi}_0 (2 sin x - sin 2x) dx$$
$$=\frac{1}{\pi} [-2 cos x + \frac{1}{2} cos 2x]^{\pi}_0$$
$$=\frac{1}{\pi} [(2+\frac{1}{2})-(-2+\frac{1}{2})] = \frac{4}{\pi}$$
(b) $$f(c) = f_{ave}, 2 sin c - sin 2c = \frac{4}{\pi}$$
$$c = c_1 \approx1.238 or c_2 \approx2.808$$
