If you know how to evaluate double integrals it's easy.
The area between f(x) and g(x) is
a and b are x coordinates, c and d are y coordinates of the intersection points of the curves.
Find the area of the circle .
Solution (analytic, not geometric ;p)
This gives us two functions of x:
So we'll find the area between these curves.
Find the x coordinates of the intersection points:
So the integral is,