qamptr
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I thought this question was elementary... but I apparently know less than I thought I did.
Use spherical coordinates to evaluate \iiint_{E} x^{2}+y^{2}+z^{2}dV
Where E is the ball x^{2}+y^{2}+z^{2}\leq 16
x^{2}+y^{2}+z^{2}=\rho^{2}
\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
which is apparently incorrect. Where am I going wrong?
Homework Statement
Use spherical coordinates to evaluate \iiint_{E} x^{2}+y^{2}+z^{2}dV
Where E is the ball x^{2}+y^{2}+z^{2}\leq 16
Homework Equations
x^{2}+y^{2}+z^{2}=\rho^{2}
The Attempt at a Solution
\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
which is apparently incorrect. Where am I going wrong?