Find the area of the region enclosed between the two circles: `x^2+y^2=4`and `(x-2)^2+y^2=4`.

Explanation

`f(x)={cos x: 0 leq x leq pi / 4 sin x: pi / 4 leq x leq 5 pi / 4 cos x: 5 pi / 4 leq x leq 2 pi} `

`A=int_{0}^{1} sqrt{4-(x-2)^{2}} d x+int_{1}^{24} sqrt{4-x^{2}} d x`

`A=[frac{sqrt{4-(x-2)^{2}}(x-2)}{2}+frac{4}{2} sin ^{-1} frac{x-2}{2}]+[frac{sqrt{4-(x)^{2}}(x)}{2}+frac{4}{2} sin ^{-1} frac{x}{2}]_{1} `

`A=2[(frac{sqrt{3}(-1)}{2}+2 sin ^{-1} frac{-1}{2})-((-2)(0)+2 sin ^{-1}(-1))+((0)+2 sin ^{-1}(1))`

`(frac{sqrt{3}(1)}{2}+2 sin ^{-1} frac{1}{2})] `

`A=2[frac{-sqrt{3}}{2}-2 sin ^{-1}(frac{1}{2})+2 sin ^{-1}(1)+2 sin ^{-1}(1)-frac{sqrt{3}}{2}-2 sin ^{-1}(frac{1}{2})] `

`A=2[-sqrt{3}-4 sin ^{-1}(frac{1}{2})+4 sin ^{-1}(1)] `

`A=2[-sqrt{3}-4(pi / 6)+4(pi / 2)] `

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