Spherical Coordinates Triple Integral

  • Thread starter qamptr
  • Start date
  • #1
10
0
I thought this question was elementary... but I apparently know less than I thought I did.

Homework Statement


Use spherical coordinates to evaluate [tex]\iiint_{E} x^{2}+y^{2}+z^{2}dV[/tex]
Where E is the ball [tex]x^{2}+y^{2}+z^{2}\leq 16 [/tex]


Homework Equations


[tex]x^{2}+y^{2}+z^{2}=\rho^{2}[/tex]



The Attempt at a Solution


[tex]\int^{2\pi}_{0}\int^{\pi}_{0}\int^{4}_{0}\left(\rho^{2}\right)\rho Sin \left( \phi \right) d\rho d\phi d\theta = 256\pi[/tex]

which is apparently incorrect. Where am I going wrong?
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
7
I thought this question was elementary... but I apparently know less than I thought I did.

Homework Statement


Use spherical coordinates to evaluate [tex]\iiint_{E} x^{2}+y^{2}+z^{2}dV[/tex]
Where E is the ball [tex]x^{2}+y^{2}+z^{2}\leq 16 [/tex]


Homework Equations


[tex]x^{2}+y^{2}+z^{2}=\rho^{2}[/tex]



The Attempt at a Solution


[tex]\int^{2\pi}_{0}\int^{\pi}_{0}\int^{4}_{0}\left(\rho^{2}\right)\rho Sin \left( \phi \right) d\rho d\phi d\theta = 256\pi[/tex]

which is apparently incorrect. Where am I going wrong?
You may want to check your volume element :wink:.
 
  • #3
10
0
You may want to check your volume element :wink:.

Am I blind? I don't understand.
 
  • #4
10
0
You may want to check your volume element :wink:.

[tex]\left(\rho^{3}\right) \rho[/tex] instead of [tex]\left(\rho^{2} \right) \rho [/tex] gets me the right answer... but why?
 
  • #5
10
0
[tex]\left(\rho^{3}\right) \rho[/tex] instead of [tex]\left(\rho^{2} \right) \rho [/tex] gets me the right answer... but why?

Oh... :rolleyes:
 

Related Threads on Spherical Coordinates Triple Integral

Replies
3
Views
2K
Replies
17
Views
6K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
2K
Replies
3
Views
2K
Replies
2
Views
2K
Replies
5
Views
2K
Replies
3
Views
3K
Replies
6
Views
5K
Top