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

find the volume of the solid generated by revolving around the x-axis: y=e^(x-8), y=0, x=0, x=10

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 11:46am
washers:

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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