Triple integral using cylindrical coordinates

[jonnyboy]

Homework Statement

\int\int_{Q}\int(x^4+2x^2y^2+y^4)dV where Q is the cylindrical solid given by \{(x,y,x)| x^2+y^2 \leq a^2, 0\leqz\leq\frac{1}{\pi}\}

Homework Equations

When I convert to cylindrical I get f(r,\theta,z) = r^4\cos^2\theta + 2r^4\cos^2\theta\sin^2\theta + r^2\sin^2\theta, but I just need the bounds for dr, is it? \int^a_0

The Attempt at a Solution

\int^2\pi_0\int^a_0\int^\frac{1}{\pi}_0 f(r,\theta,z)rdzdrd\theta
*the first integral is supposed to be from 0 to 2pi

 

[gabbagabbahey]

Your expression for f(r,\theta,z) is incorrect. It might help you to realize that f(x,y,z)=x^4+2x^2y^2+y^4=(x^2+y^2)^2...so f(r,\theta,z)=?

And yes, r goes from 0 to a.

 

[jonnyboy]

Got it, so f(r,\theta,z) = r^4 Much simpler!