Question: I'm having problems with starting this integral, I'm not looking for the solution, but the first step/two would be appreciated. 

**Integral**:

Evaluate 

$$
\int dx \sqrt{x(4-x)}
$$

Answer: 
Hint: $ \displaystyle \int \sqrt{ 4 - 4 + 4x - x^2} dx$

$ = \displaystyle \int \sqrt{ 2^2 - (x-2)^2}dx$

Now use the formula - $ \displaystyle \int \sqrt{a^2 - x^2} dx$

This should be enough
Sub $x=4 \sin^2{t}$, $dx = 8 \sin{t} \cos{t} \, dt$, so the integral becomes

$$32 \int dt \sin^2{t} \cos^2{t} $$

That should be enough of a hint.