Wednesday

July 30, 2014

July 30, 2014

Posted by **Anonymous** on Tuesday, January 29, 2013 at 11:10pm.

So I know you can use the washer method, but the shell method can also be used and it should be better. The issue is I'm not certain how to actually do it. Any help is appreciated!

- calc -
**Steve**, Wednesday, January 30, 2013 at 11:46amwashers:

v = ∫[0,10] πr^2 dx

where r = y = e^(x-8)

v = π∫[0,10] (e^(x-8))^2 dx

= π∫[0,10] e^(2x-16) dx

= π/2 e^(2x-16) [0,10]

= π/2 (e^4 - 1/e^16)

shells:

y = e^(x-8), so x = 8+lny

v = ∫[e^-8,e^2] 2πrh dy

where r = y and h = 10-x = 2-lny

v = 2π∫[e^-8,e^2] y(2-lny) dy

= π/2 (y^2(5-2lny)) [e^-8,e^2]

= π/2 (e^4 - 21/e^16)

Hmmm. better double-check my math. Anyway, that's the method.

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