Posted by **Anonymous** on Wednesday, December 12, 2012 at 4:35am.

Have mercy!

Find the volume of the solid obtained by rotating y=3+2x-x^2, x+y=3 about the y-axis.

- Math Calculus 1 -
**Steve**, Wednesday, December 12, 2012 at 5:23am
better integrate on x, since doing discs on y will need to separate the region into two pieces. So, using shells,

v = ∫[0,3] 2πrh dx

where r = x and h = (3+2x-x^2) - (3-x)

v = 2π∫[0,3] x((3+2x-x^2) - (3-x)) dx

= 2π∫[0,3] 3x^2-x^3 dx

= 2π(x^3 - x^4/4) [0,3]

= 27/2 π

- Math Calculus 1 -
**Anonymous**, Wednesday, December 12, 2012 at 5:50am
Thank you!!!

- Math Calculus 1 -
**Anonymous**, Wednesday, December 12, 2012 at 6:03am
If you would check my last 2 questions. I am just completely stumped.

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display.cgi?id=1355309813

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