Triple Integral in Cylindrical Coordinates

[daveyman]

Homework Statement

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 $$z^2=4x^2+4y^2$$.

Homework Equations

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

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?

 

[tiny-tim]

… above the plane $$z=0$$
…
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.

Hi daveyman!

z goes from zero to 2r.

 

[daveyman]

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