Calculus II - Volume By Shells

Hello, having some problems with a volume by shells problem. I believe my issue is the setup.

Question: Use the shells method to find the volume of a solid generated by revolving the region bounded by the lines y=x+6 and y=x^2 about the following lines;

a) The line x=3
b) The line x=-2
c) The x-axis
d) The line y=9

So - I convert;

y = x+6
x = y-6

y = x^2
x = sqrt(y)

Rest coming in an equation post -

Question

Calculus II - Volume By Shells

Hello, having some problems with a volume by shells problem.  I believe my issue is the setup.

Question: Use the shells method to find the volume of a solid generated by revolving the region bounded by the lines y=x+6 and y=x^2 about the following lines;

a) The line x=3
b) The line x=-2 
c) The x-axis
d) The line y=9

So - I convert;

y = x+6
x = y-6

y = x^2
x = sqrt(y)

Rest coming in an equation post -

anonymous · Answer

$$2\pi  \int\limits_{0}^{9} (3-x)(\sqrt(y) - (y-6))$$

Is this the correct setup?

turingtest · Answer

for a ?

anonymous · Answer

Yeah, sorry.

turingtest · Answer

well I would set it up the other way, in terms of x...

anonymous · Answer

That was a typo, I meant to have (3-y)(sqrt(y) etc, etc...

turingtest · Answer

|dw:1327780091605:dw|$$2\pi\int_{-2}^{3}(3-x)[(x+6)-x^2]xdx$$is the way I see it easiest...