Using integration find the area of that part of circle x²+y²=16, which is exterior to the parabola y²=6x

We have to find the area of that part of circle x²+y²=16, which is exterior to the parabola y²=6x. So, we have to find the shaded region area.

Firstly, we will find the point of intersection,

So

And

So, the point of intersection are , and. We will take only first and second point because third point has imaginary value.

Required area= area of circle – area of the part which is not shaded

So,

And

Now, substitute all values in equation (1), we get,