# Integral Help: Completing the square?

1. Feb 12, 2008

### nickclarson

1. The problem statement, all variables and given/known data

$$\int^{3}_{0}\frac{x^{2}}{(25-4x^{2})^{\frac{3}{2}}} dx$$

2. Relevant equations

3. The attempt at a solution

Not sure on where to start. We learned in class how to complete the square, but i'm not sure if that's what I am supposed to use on this problem. Can anybody give me a hint on where to start? it would be greatly appreciated.

Thanks,
Nick
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Feb 12, 2008
2. Feb 12, 2008

### Gib Z

Here I would use a trig substitution. Also, you forgot the "dx" term. It is very important.

We have;

$$\int^3_0 \frac{x^2}{ ( 5^2 - (2x)^2)^{3/2}} dx$$

Can you think of a trig substitution that would make that denominator simpler?

3. Feb 12, 2008

### nickclarson

Oh yea whoops, hmm. $$x= asin\theta$$? I'll give it a shot and see what happens. Thanks!