• Support PF! Buy your school textbooks, materials and every day products via PF Here!

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

  • Thread starter VinnyCee
  • Start date
489
0
Here is the problem:

Find the volume of the region enclosed by the spherical coordinate surface [tex]\rho = 2 \sin\theta[/tex], 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 [tex]\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[/tex]
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,950
532
It looks okay.Did u plot it?Heh,u we use [itex] r,\varphi,\vartheta [/itex] as the spherical coordinates...:wink:

Daniel.
 
489
0
Whoops!

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

[tex]\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[/tex]

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

Science Advisor
Homework Helper
Insights Author
12,950
532
No,it looks okay.

Daniel.
 

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

  • Posted
Replies
7
Views
824
Replies
1
Views
755
Replies
2
Views
248
Replies
1
Views
3K
Replies
6
Views
1K
  • Posted
Replies
1
Views
2K

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
Top