# Homework Help: Triple Integral

1. May 24, 2017

### namehere

• Moved from a technical forum and thus no template
Here on problem #13 i am getting a false solution when only taking the volume of the region in quadrant 1 and multiplying it by 4. The later photo contains the correct solution which is obtained by taking the volume of the entire region. Can someone explain to me why the former is incorrect.

2. May 24, 2017

### LCKurtz

Just because you are calculating a triple integral, it doesn't mean you are calculating a volume. If the integrand was $1$, you would be, and your method would be correct. But your integrand is $x^2e^y$, and $e^y$ is not symmetric about $y=0$. So you don't get the same answer for each quadrant.

3. May 25, 2017

### Ray Vickson

4. May 27, 2017

### Eclair_de_XII

I tried the problem myself. Is anyone else getting $\frac{8}{3}e^{-1}$?

5. May 27, 2017

### LCKurtz

Yes, that's correct.