Using integration, find the area of the region common to the circle `x^2+y^2=16` and the parabola `y^2=6x`.

Explanation

Here, The given curves are

`x^{2}+y^{2}=16 quad cdots (1)`

And` x^{2}=6 y quad cdots (2)`

On solving equation (1) and (2), we get

A`(-2 sqrt{3}, 2) and B(2 sqrt{3}, 2)`

`Required area =2( Area {OBCO})`

`=2[ Area ODBCO - Area ODBO ]`

`=2[int_{0}^{2 sqrt{3}} sqrt{16-x^{2}} d x-int_{0}^{2 sqrt{3}} frac{x^{2}}{6} d x]`

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