# Am I setting this integral up correctly?

1. Oct 20, 2015

### SarahAlbert

1. The problem statement, all variables and given/known data
Use spherical coordinates to evaluate the integral over a sphere of radius R.

2. Relevant equations
The equation of my sphere would be x^2+y^2+z^2=R^2

3. The attempt at a solution
I have attached a file to show my work so far. Evaluating the integral once it is set up should be fine, I'm concerned it's not set up correctly. Thank you.

#### Attached Files:

• ###### Screen Shot 2015-10-20 at 1.38.54 AM.png
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2. Oct 20, 2015

### BvU

Hello,
You want to reconsider dV. $\ \ \ dV \ne dr\, d\phi \,d\theta$.

3. Oct 20, 2015

### SarahAlbert

I'm beginning to think that it's also not as easy as (pcos∂)^2 since my radius is R then p=R so isn't it ∫∫∫pcos∂)^2p^2

4. Oct 20, 2015

### PWiz

Nope. You're integrating p over a radius of R. It's not the same thing.

5. Oct 20, 2015

### BvU

You are calculating a volume integral, so your p is running from 0 to R .

Your function to integrate is $\ f(r, \theta, \phi) = (r\cos\theta)^2$ as you wrote correctly.

Now check out how you can express a volume element in spherical coordinates $dV(r, \theta, \phi)$ , e.g. as shown here or here

6. Oct 20, 2015

### SarahAlbert

So it would then be (rcosθ)^2r^2sinθdrdθdphi which becomes r^2sinθcosθdrdθdphi and then become r^2sin(2θ)/2drdθdphi