Question

Integrate x^2+y^2+z^2 over the cylinder x^2+y^2 ≤2, 2≤z≤3. are the bounds of the cylinder the bounds you integrate by?

Answer 1

yes, in cylindrical coordinates (x,y,z,) becomes (r, theta, z)
r goes from 0 to 2
theta goes from 0 to 2pi
z goes from 2 to 3
so those are your bounds

Answer 2

ok thanks just wanted to make sure i was on the right track. thanks again!

Answer 3

so would my integration look like this?
\[\int\limits_{2}^{3}\int\limits_{0}^{2}\int\limits_{0}^{2\Pi} r+z^2 dzdrd \Theta\]