Hi. I'm trying to do the integral Leibniz solved when he calculated pi. It goes as follows:

$\displaystyle I=\int_0^1 \sqrt{2x-x^2}\rm{d}x=\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{2n-1}=\frac{\pi}{4}$

I know the solution to the integral, but I can't solve it.

Can somebody please show me how this integral is solved?

Thanks in advance.