Sorry I do not have a 3-d grapher, so accept my hand drawing, on the bottom.
So we are finding,
Which by Fubini's theorem is,
Where is your region.
Which is,
#14 f(x,y,z) = z W is the region in the first octant bounded by the cylinder y^2 + z^2 = 9 and the planes y = x, x = 0 and z = 0
My first intergral has the limits between x = 0 and x = y^2 + z^2 - 9
My second intergral has limits between z = 0 and z = sqrt(9-y^2)
My final intergral ranges in between y = 0 and y = 3
I dont think it right because I end up with a negative answer
I end up with -162/5
What am I doing wrong????????????????????????