# Thread: Spherical Coordinates Concept Question

1. ## Spherical Coordinates Concept Question

I'm in the process of studying for a test next week and I have a review question I cannot answer. The problem asks to evaluate the integral by changing to spherical coordinates.

I am only looking for what the actual integral would be in spherical coordinates, I don't actually need you to evaluate the integral.

The triple integral in rectangular coordinates is:

If you can, please provide an overview of what the sphere would look like.

Thanks!

2. Originally Posted by 360modina
I'm in the process of studying for a test next week and I have a review question I cannot answer. The problem asks to evaluate the integral by changing to spherical coordinates.

I am only looking for what the actual integral would be in spherical coordinates, I don't actually need you to evaluate the integral.

The triple integral in rectangular coordinates is:

If you can, please provide an overview of what the sphere would look like.

Thanks!
Everything you need is here: Spherical Coordinates -- from Wolfram MathWorld

Almost everything ........ Note that your lower and upper integral terminals for r are 0 and a respectively (since the volume you're integrating over is a sphere of radius a).

3. I ran through the problem as a normal sphere centered at (0, 0, 0) with a

$\displaystyle 0\eqslantless\rho\eqslantless a$
$\displaystyle 0\eqslantless\theta\eqslantless\pi$
$\displaystyle 0\eqslantless\phi\eqslantless 2\pi$

and integrated in the order
$\displaystyle d\rho \ d\theta \ d\phi \$

and tacked a $\displaystyle (\rho)^2 \sin \phi$ on the end to account for the spherical conversion.

When I solve the problem I get with the mess of the (x^2*z+z...) spherical converted mess in there I end up with an answer of 0 and the same holds when I evaluate the original by hand in rectangular coordinates. Any thoughts?