Posted by **marks** on Sunday, March 16, 2014 at 2:30pm.

using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1

- calculus -
**Steve**, Sunday, March 16, 2014 at 4:52pm
for shells, we need to integrate on y, since the area is rotated about a horizontal line, and the shells have thickness dy

v = ∫[1,2] 2πrh dy

where r = y-1 and h = x = ln y

v = 2π∫[1,2] (y-1)lny dy

Just use integration by parts to evaluate it.

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