Spherical coordinates

  • Thread starter mrkb80
  • Start date
  • #1
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Homework Statement



I am having so much trouble with this one problem ( and spherical coordinates in general ).

Any help would be amazing:
∫∫∫ 1 / √(x2+y2+z2)

Over -4≤x≤4, 0≤y≤√(16-x2), 0≤z≤√(16-x2-y2)


Homework Equations





The Attempt at a Solution


I know that rho2 will replace √(x2+y2+z2) in my integral, but I am having a really hard time understanding what my limits of integration should be for rho,phi, and theta. I think it is some sort of a snow cone, where theta is from 0 to pi/2 but I'm really not sure.
 

Answers and Replies

  • #3
557
1
Your volume is a quarter of a ball. A ball cut in 4 pieces by two ortogonal planes.
This is 0<rho<4, 0<theta<pi, 0<phi<pi/2
 

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