How to setup an integral in spherical coordinates for the volume of p = 2 sin O(theta

VinnyCee

Here is the problem:

Find the volume of the region enclosed by the spherical coordinate surface $$\rho = 2 \sin\theta$$, using spherical coodinates for the limits of the integral.

Here is what I have:

I don't know if this is right, but here it is $$\int_{0}^{2\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\int_{0}^{2\sin\theta}\;\rho^2\;\sin\theta\;d\rho\;d\phi\;d\theta$$

Related Introductory Physics Homework Help News on Phys.org

dextercioby

Homework Helper
It looks okay.Did u plot it?Heh,u we use $r,\varphi,\vartheta$ as the spherical coordinates... Daniel.

VinnyCee

Whoops!

I posted the wrong thing. Instead of $$2\sin\theta$$ for the first integrals upper limit, it should be $$2\sin\phi$$?

$$\int_{0}^{2\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\int_{0}^{2\sin\phi}\;\rho^2\;\sin\theta\;d\rho\;d\phi\;d\theta$$

So confusing!

Is that wrong now?

The graph looks like a donut without the hole centered at the origin. I will post it shortly.

dextercioby

Homework Helper
No,it looks okay.

Daniel.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving