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Q14E

Expert-verifiedFound in: Page 369

Book edition
2nd

Author(s)
James Stewart

Pages
830 pages

ISBN
9781133112280

**Sketch the region enclosed by the given curves and**

**find its area. **

**14. y = cosx, y = 2 - cosx, 0 ≤x≤2𝛑 **

The Area\( = 4\pi \)** **

Graph is shown,

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

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

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

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

\( = 4\pi \)** **

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