Find the area of the region in the first quadrant enclosed by the x-axis, the line `y = x`, and the circle `x^2+y^2=32`.

Find the area of the region in the first quadrant enclosed by the x-ax

1.	Find the area of the region in the first quadrant enclosed by the x-axis, the line `y = x`, and the circle `x^2+y^2=32`.
Answer» Required area `=underset(4)overset(0)int xdx+underset(4)overset(4sqrt(2))int sqrt(32-x^2)dx` `=[x^2/2]_0^4+[(xsqrt(32-x^2))/2+32/2sin^-1""x/(4sqrt(2))]_4^(4sqrt(2))` `4 pi` sq units