Question

\[\int_0^{2\pi}\int_0^{pi/4}\int_0^4(\rho\cos\phi)\rho^2\sin\phi \ \ d\rho \ \ d\phi \ \ d\theta \]

Answer 1

:-( I should have picked medicine over engineering

Answer 2

first compute this by treating fi as a constant:
\[\int_0^4(\rho\cos\phi)\rho^2\sin\phi \ \ d\rho\]

Answer 3

so sin(phi) is taken out?

Answer 4

\[\int_0^4(\rho\cos\phi)\rho^2\sin\phi \ \ d\rho=sin\phi cos\phi\int_0^4\rho^3 \ d\rho\]
if I read it correctly