
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(9y^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????????????????????????

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Sorry I do not have a 3d grapher, so accept my hand drawing, on the bottom.
So we are finding,
$\displaystyle \int \int_V \int z \, dV$
Which by Fubini's theorem is,
$\displaystyle \int_A \int \int_0^{\sqrt{9y^2}} z \, dz\, dA$
Where $\displaystyle A$ is your region.
Which is,
$\displaystyle \int_0^3 \int_x^3 \int_0^{\sqrt{9y^2}} z\, dz\, dy\, dx$