- #1
qamptr
- 10
- 0
I thought this question was elementary... but I apparently know less than I thought I did.
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]
[tex]x^{2}+y^{2}+z^{2}=\rho^{2}[/tex]
[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?
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?