1. ## Triple Intergral

#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????????????????????????

2. Sorry I do not have a 3-d grapher, so accept my hand drawing, on the bottom.

So we are finding,
$\int \int_V \int z \, dV$
Which by Fubini's theorem is,
$\int_A \int \int_0^{\sqrt{9-y^2}} z \, dz\, dA$
Where $A$ is your region.
Which is,
$\int_0^3 \int_x^3 \int_0^{\sqrt{9-y^2}} z\, dz\, dy\, dx$