# A quick triple integral

1. May 23, 2005

### MaximumTaco

Firstly, can someone please demonstrate the proper Latex code for the terminals on a multiple integral? Thanks!

Anyway, as you can probably see, i'm calculating the volume enclosed by x^2+y^2+z^2 = 2 and z = x^2+y^2 using a change to cylindrical coordinates.

$$V = \iiint_{0}^{2\pi}_{0}^{\sqrt{2}}_{\rho^2}^{\sqrt{2-\rho^2}} \rho dz\,d\rho\,d\phi$$

Is that integral right?

The answer i get when evaluating the integral is (pi/3)(4sqrt(2) - 6), which is the same doing it by hand or using Mathematica. But it doesn't agree with the expected answer.

Last edited: May 23, 2005
2. May 23, 2005

### dextercioby

$$V=\int_{0}^{1}\rho \ d\rho \int_{0}^{2\pi} d\varphi \int_{0}^{\rho^{2}} dz$$

Daniel.