6.1 Areas Between Curves/14

${\begin{aligned}&\color {purple}\mathbf {y=\cos(x)} ,y=2-\cos(x)\\&\int _{0}^{2\pi }\left[2-\cos(x)-\cos(x)\right]\mathrm {d} x=\int _{0}^{2\pi }\left[2-2\cos(x)\right]\mathrm {d} x\\&=\left[2x-2\sin(x)\right]{\bigg |}_{0}^{2\pi }\\&=\left(4\pi -0\right)-\left(0\right)\\&=4\pi \end{aligned}}$