# Complicated double integral

1. Oct 28, 2012

### Hernaner28

1. The problem statement, all variables and given/known data
I've got to calculate:

$$\displaystyle\int_0^1\displaystyle\int_0^x \sqrt{4x^2-y^2} dy dx$$

2. Relevant equations

3. The attempt at a solution

I've tried the change of variable:
$$\displaystyle t=4{{x}^{2}}-{{y}^{2}}$$ but it doesn't get better. I've also tried polar coordinates but it is not convinient either. Do you know a convenient change? I've been trying to figure it out for a long time.

** I also tried changing the order of integration but no results.

Thanks!

2. Oct 28, 2012

### Ray Vickson

The y-integral (for any fixed value of x) is of the form
$$\int \sqrt{a^2 - y^2} \, dy,$$
where it happens that a = 2x. This is a standard integral that you must surely have seen before; if not, do a change of variables using a trigonometric substitution.

RGV

Last edited: Oct 28, 2012
3. Oct 28, 2012

### Hernaner28

Thanks! I'll try!