# Triple integral using cylindrical coordinates

## 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

Last edited:

gabbagabbahey
Homework Helper
Gold Member
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.

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