Question

Sketch the region enclosed by the given curves and

find its area.

14. y = cosx, y = 2 - cosx, 0≤x≤2𝛑

Short answer

The Area\( = 4\pi \)

Step-by-step solution

The given curves

Graph is shown,

Substitute the integral to find the area

\(y = \cos x\) is below for the entire interval. Subtract from the other function in the integral to find the area.

\(A{\rm{ }} = _0^{2\pi }(2 - \cos x - \cos x)dx = \;\;\;0_0^{2\pi }(2 - 2\cos x)dx\)

\( = (2x - 2\sin x)_0^{2\pi }\)

\( = 4\pi - 0 - (0 - 0)\)

\( = 4\pi \)