I am examining:
$$\int_0^1 (1-ax)^{1/2} dx$$
If we differentiate:
$$\dfrac{d}{dx} \left[\dfrac{-2(1-ax)^{3/2}}{3a}\right]$$
we get to the function in the integral. The idea now is consider various values for $a$, for example $a=1$ but more specifically $a=x$.
Only thing is that I am fairly sure I'm doing something wrong, because I can't see how the integral is going to return $\pi$.