# Triple integral

• Jun 10th 2009, 11:09 AM
sillyme
Triple integral
$\int\!\!\!\!\int\!\!\!\!\int_V e^{{(x^2+y^2+z^2)}^{\frac{3}{2}}}dxdydz$ where $V=\{(x,y,z)|x^2+y^2+z^2\leq1\}$
I tried switching to spherical coordinates:
$x=r\cos\varphi\sin\theta$
$y=r\sin\varphi\sin\theta$
$z=r\cos\theta$
$dV=r^2 \sin \theta dr d \theta d\varphi$
with $0\leq r\leq1$ but I'm not sure about the range of $\varphi$ and $\theta$
• Jun 10th 2009, 11:21 AM
Amer
Quote:

Originally Posted by sillyme
$\int\!\!\!\!\int\!\!\!\!\int_V e^{{(x^2+y^2+z^2)}^{\frac{3}{2}}}dxdydz$ where $V=\{(x,y,z)|x^2+y^2+z^2\leq1\}$
I tried switching to spherical coordinates:
$x=r\cos\varphi\sin\theta$
$y=r\sin\varphi\sin\theta$
$z=r\cos\theta$
$dV=r^2 \sin \theta dr d \theta d\varphi$
with $0\leq r\leq1$ but I'm not sure about the range of $\varphi$ and $\theta$

$0\leq\varphi\leq2\pi , 0\leq\theta\leq \pi ,0\leq\rho\leq1$ now it is correct

Edited:- Spec show me mistake that I did
• Jun 10th 2009, 12:00 PM
Spec
Actually, with those variables the limits are $0\leq \varphi \leq 2\pi,\ 0\leq \theta \leq \pi$

It can be a bit confusing since a lot of sources use different variables for the angles.
• Jun 10th 2009, 12:04 PM
Amer
Usually I use $\phi$ instead of $\theta$ so I didn't look to what he write thanks to Spec