## Calculus: Early Transcendentals 8th Edition

$$A = 4\pi$$
$y=\cos x$ is below the entire interval; subtract from the other function in the integral to find the area. $$\displaystyle\int_{0}^{2\pi}(2-\cos x - \cos x)dx = \displaystyle\int_{0}^{2\pi} (2-2\cos x)dx$$ $$= \left[2x-2\sin x \right]^{2\pi}_0$$ $$=4\pi - 0 - (0-0)$$ $$= 4\pi$$