# Volume Using Shells

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• Oct 21st 2008, 03:40 PM
sfgiants13
Volume Using Shells
I can do volume fine about x and y=0, but I get messed up when it's about somewhere other than those.

x+y=3, x=4(y-1)^2...Find the area rotating about the x axis.

Can someone point me in the right direction?
• Oct 21st 2008, 04:54 PM
skeeter
Quote:

Originally Posted by sfgiants13
I can do volume fine about x and y=0, but I get messed up when it's about somewhere other than those.

x+y=3, x=4(y-1)^2...Find the area rotating about the x axis.

Can someone point me in the right direction?

I'm guessing you really mean the volume ...

$3-y = 4(y-1)^2$

$3-y = 4y^2 - 8y + 4$

$0 = 4y^2 - 7y + 1$

$y = \frac{7 \pm \sqrt{33}}{8}$

let $c = \frac{7 - \sqrt{33}}{8}$

$d = \frac{7 + \sqrt{33}}{8}$

$V = 2\pi \int_c^d y[(3-y) - 4(y-1)^2] dy$