# Thread: Triple integral with cylindrical coordinates

1. ## Triple integral with cylindrical coordinates

I need to evaluate the triple integral over the region W of:

f(x,y,z) = x^2 + y^2 + z^2 where W is the region r greater than or = to 0 and less than or = to 4, theta greater than or = tp pi/4 and less than or = to 3pi/4, z greater than or = to -1 and less than or less than 1

using those limits I integrated (r^2 + z^2) r dr dtheta dz is this correct?

2. Originally Posted by Frostking
I need to evaluate the triple integral over the region W of:

f(x,y,z) = x^2 + y^2 + z^2 where W is the region r greater than or = to 0 and less than or = to 4, theta greater than or = tp pi/4 and less than or = to 3pi/4, z greater than or = to -1 and less than or less than 1

using those limits I integrated (r^2 + z^2) r dr dtheta dz is this correct?
Yes. The integral you're integrating should be $\displaystyle \int_{-1}^1\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \left(r^3+z^2r\right)\,dr\,d\theta\,dz$