Hello,

I keep getting this volume wrong by a factor of 4... I keep ending up with $\displaystyle 16 \ pi \sqrt{3}$ instead of $\displaystyle 4\pi \sqrt{3}$. Could someone please tell me what's wrong in my integral?

Question is: Find the volume that is inside $\displaystyle x^2+y^2+z^2=4$ but outside $\displaystyle x^2+y^2=1$.

My integral is $\displaystyle \int_0^{2\pi} \int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} \int_{\frac{1}{\sin \phi}}^2 \rho^2 \sin \phi d \phi d \rho d \theta$.

Thanks

EDIT: I've figured out how to do this problem... Took quite a bit though... So I don't need help on this problem anymore