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

Very quick triple integral question

  • Thread starter narfarnst
  • Start date
14
0
1. Homework Statement
Use the Divergence Theorme to evaluate the flux of v(x,y,z)=[tex]x^{2}[/tex]i+[tex]y^{2}[/tex]j+[tex]z^{2}[/tex]k on the solid T bounded above by a sphere with radius 3 and below by the xy-plane.
I've found that div(v) is 2(x+y+z).

When I go to set up the integral I get a triple integral over T of (x+y+z)dV (and I bring the 2 outside the integral). So, of course, I switch to spherical coordinates.
Now, my question. When I do the switch, can I treat (x+y+z) as sqrt(r), or do I actually have to plug in the parametrized x, y, and z and evaluate?

Thanks.
 

tiny-tim

Science Advisor
Homework Helper
25,790
249
hi narfarnst! :smile:

(have a square-root: √ :wink:)
… I get a triple integral over T of (x+y+z)dV (and I bring the 2 outside the integral). So, of course, I switch to spherical coordinates.
Now, my question. When I do the switch, can I treat (x+y+z) as sqrt(r), or do I actually have to plug in the parametrized x, y, and z and evaluate?
but it isn't √r ! :rolleyes:

so, yes, you do actually have to do the work! :smile:
 

Related Threads for: Very quick triple integral question

Replies
6
Views
1K
Replies
7
Views
929
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
995
Replies
3
Views
948
Top