# Integral homework problem help

1. Apr 30, 2006

### -=nobody=-

$$2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx$$
Can you help me with this integral?

2. Apr 30, 2006

### arildno

You have already been advised to do a change of variables, rather than do this in Cartesian variables.

3. Apr 30, 2006

### -=nobody=-

4. Apr 30, 2006

### arildno

Well, how would you go about proving that the unit ball has volume $\frac{4}{3}\pi$ ?

5. Apr 30, 2006

### -=nobody=-

Well, the idea is probably good, but it doesn't help me with the integral

6. Apr 30, 2006

### HallsofIvy

Staff Emeritus
Well, the idea is just to use spherical coordinates. Have you sketched the region over which that integral is taken? Looks to me like there is a heckuvalot of symmetry there!

7. May 1, 2006

### -=nobody=-

Won't it be much more complicated, or is it the only way?
r=(x^2+y^2+z^2)^1/2.

Last edited: May 1, 2006
8. May 1, 2006

### -=nobody=-

It's clear that there is symmtry, but if r=(x^2+y^2+z^2)^1/2 everything will be much more complicated. How should it be solved then?

9. May 1, 2006

### -=nobody=-

Sorry for this post, I had some problems with my internet browser.

10. May 1, 2006

### siddharth

$$x= a r \cos\theta$$
$$y = b r\sin \theta$$
Now, find the Jacobian and limits of integration of $\theta$ and $r$. Can you take it from here?