Integral of $\sqrt{ax-x^2}$ Can we integrate a function of the form $$\sqrt{ax-x^2},\text{say for any limits a to b}$$
I was solving a question recently where I had to find the volume and the eqn of base was $$x^2+y^2=ax\implies\,(x-\frac{a}{2})^2+y^2=\frac{a^2}{4}$$
now although it is easy to integrate this when writing x in terms of y, i tried to write y in terms of x and got the equation written above and was stuck as to how to integrate that form

Hint 
Substitute $x=a\cos^2(u)$
with $dx=-2a\cos(u)\sin(u) du =-a\sin(2u)du $
$\sqrt{ax-x^2}=\sqrt {a^2\cos^2(u)-a^2\cos^4(u)}=a \cos(u)\sin(u)=\frac a 2 \sin(2u)$
then,
$$I=\frac {-a^2} 2 \int \sin^2(2u)du$$
