Is there any elementary reasoning to get $\displaystyle \displaystyle\int^1_0 \sqrt{x(1-x)}\ dx = \pi/8$? The actual antiderivative is too long, and I don't think computing it is the right approach for the question I am working on. Could there be a polar coordinate transformation? Since the answer has a $\displaystyle \pi$ in it. I just need a tiny hint, thanks.