# Math Help - Triple Integral

1. ## Triple Integral

I am having trouble with the following triple integral:

Triple Integral (over E), where E is bounded by the cylinder (y^2) + (z^2) = 9, and the planes x = 0, y = 3x, and z = 0. The density function of the triple integral is defined as f(x, y, z) = z dV.

The biggest problem I am having is defining the boundaries for each integral (i.e. iterating the integral).

Thanks for any help.

2. So I made a picture of the graph and came up with the domain lying in the xy plane. It was bounded by x = 0 and y=3x and y = 3.

y=3 comes from when z = 0 in the xy plane, $y^2 = 9, y = 3$

So it forms a triangle. It is vertically linear, so y ranges from 0 to 3, x ranges from 0 to y/3. Then finally z ranges from 0 to $sq(9-y^2)$

Then all you have to do is integrate.