 Hello friends and how are you all doing today? The question says, using integration find the area of the circle x square plus y square is equal to 16 which is exterior to the parabola y square is equal to 6x. Now here in this question we have in the first quadrant the point of intersection of the circle x square plus y square equal to 16 and the parabola y square equal to 6x is let's say point B which is 2, 2 root 2. x is 2 and y is 2 root 2. Now here we need to find out the area of the circle which is exterior to the parabola. So the required area over here is say A, area of the circle minus area of circle interior to parabola. Now area of the circle is pi r square here r is 2 so area of the circle will be pi sorry the radius of the circle is not 2 but it is 4 so it is pi 4 square minus area of the circle which will be the exterior to the parabola will be 2 integral 0 to 2 y dx minus 0 2 to 4 integral y dx. So what we need to do is we just need to simplify this expression. So we have it as 16 pi minus 2 integral 0 to 2 the value of y will be root 6x raised to the power 1 by 2 dx and for this one again it will be from 2 to 4 under root 16 minus x square. Now here we have substituted the value of y of this we substituted the value of y that is the value of y of this parabola. So we have 16i minus 2 root 6. Now here after solving this integral we have 2 by 3 x raised to the power 3 by 2 0 to 2 minus 2. Now here this integral this is of the special type a square minus x square. So we have the formula as x under root 16 minus x square upon 2 plus 16 sin inverse x by 4 0 to sorry 2 to 4 which can be solved further 16 pi minus its value can be written as 16 by root 3 minus 8 pi plus 4 root 3 plus 8 pi by which is further equal to 4 by root 3 plus 32 pi by 3 which can be further written as equal to 4 by 3 bracket taking 8 pi minus root 3 common square units. So this is the required answer to the given question. You understood it well and enjoyed it too have a nice day.