Triple Integral in Cylindrical Coordinates

1. Nov 9, 2008

daveyman

1. The problem statement, all variables and given/known data
Evaluate $$\int \int \int_E x^2 \, dV$$ where E is the solid that lies within the cylinder $$x^2+y^2=1$$, above the plane $$z=0$$, and below the cone $$z^2=4x^2+4y^2$$.

2. Relevant equations
In cylindrical coordinates, $$x^2+y^2=r^2$$ and $$x=r\cos{\theta}$$.

3. The attempt at a solution
I tried $$\int _0^{2\pi }\int _0^1\int _{-2r}^{2r}r^2 cos^2\theta\;\;r\;\;dzdrd\theta$$ but I must have messed up the bounds somehow.

Any ideas?

2. Nov 10, 2008

tiny-tim

Hi daveyman!

z goes from zero to 2r.

3. Nov 10, 2008

daveyman

Of course - it says it right in the problem :-) Thanks!