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!