y = cos ( x ) , y = 2 − cos ( x ) ∫ 0 2 π [ 2 − cos ( x ) − cos ( x ) ] d x = ∫ 0 2 π [ 2 − 2 cos ( x ) ] d x = [ 2 x − 2 sin ( x ) ] | 0 2 π = ( 4 π − 0 ) − ( 0 ) = 4 π {\displaystyle {\begin{aligned}&\color {purple}\mathbf {y=\cos(x)} ,\color {green}\mathbf {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}}}
![{\displaystyle {\begin{aligned}&\color {purple}\mathbf {y=\cos(x)} ,\color {green}\mathbf {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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/5a4883cde5389d4f0c60fca6be39df1c59efb457)
