# Calculating Triple Integrals in Mathematica

1. May 3, 2013

### november1992

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

Evaluate ∫∫∫$\sqrt{x^{2} + y^{2}}$ dA where R is the region bounded by the paraboloid y=x^2+z^2 and the plane y=4

2. Relevant equations
I believe this is a problem where cylindrical coordinates would be useful

0 ≤ z ≤ $\sqrt{4-x^2}$
0 ≤ r ≤ 2 ( I think this is wrong).
0 ≤ θ ≤ 2$\pi$

3. The attempt at a solution

Integrate[ r^2, {\[Theta], 0, 2*Pi}, {r, 0, 2}, {z, 0, Sqrt[4 - r*Cos[\[Theta]]^2]}]

There isn't an output when I enter this line. I checked for the syntax on the wolfram reference page so I think the problem is with the limits of integration.

2. May 3, 2013

### SteamKing

Staff Emeritus
What is the source of your integral? What is it supposed to represent? I say this because you have a triple integral with dA rather than dV.

3. May 4, 2013

### november1992

This problem was given to me by my instructor.

4. May 4, 2013

### SteamKing

Staff Emeritus
Yeah, I figured it wasn't revealed to you in a dream. But what is the ultimate source of this integral? Is it a problem out of a book? Have you solved faster than light travel? Is a new mathematics about to be revealed to us?

You realize, I hope, that there seems to be something missing: You have a triple integral of a function with respect to what appears to be a differential element of area dA. Three integrations, two variables with respect to which the integration could be carried out. It's not clear how this integral is supposed to be calculated.