Use a definite integral to find the area of the upper right quarter of the circle of radius 1 with the centre at the origin of the coordinate plane.
(the integration of √1 − x^2dx =1/2(x√1 − x^2 + arcsin x)).
well, shoot - you already have the function, so just evaluate it at 0 and 1
1/2 [1√(1 - 1)+arcsin(1))-(0√(1-0)+arcsin(0))] = 1/2 [(0 + π/2)-(0+0)] = π/4