# Triple Integral

1. Jul 21, 2009

### Ions

Problem: Evaluate (leave in rectangular coordinates):
$$\int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz\,dy\,dx$$

2. Jul 21, 2009

### n!kofeyn

Well, start slow. Can you evaluate this integral?
$$\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz$$

3. Jul 21, 2009

### Ions

$$2\int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\2{\sqrt{1-x^2-y^2}}}\,dy\,dx$$

Supposedly it's easier to make a subtitution u = 1-x^2 at this point but I don't see how...

Last edited: Jul 21, 2009