Area between curves

**andrewho93** · October 13th 2010, 08:56 PM

Find the region between y=e^x and y=e^-x rotated around the y axis. The bound is x=1. Would I use shell method for this or washer?

**yannyy** · October 13th 2010, 09:04 PM

shells

**HallsofIvy** · October 14th 2010, 04:38 AM

Shells would work. I don't see how "washers" would be used here.

You could also do this is two separate parts. When x= 1, y= $y= e^{-x}= e^{-1}$ is a bound and at x=-1, $y= e^x= e^{-1}$ is a bound. That is, for y= 0 to $y= e^{-1}$ the right and left bounds of the area are the straight lines x= 1 and x= -1. The figure is a cylinder, having area $\pi r^2 h= \pi(1)^2 e^{-1}= \pi e^{-1}$ . You can do the volume from $y= e^{-1}$ up to y= 1 (where the two graphs intersect) by discs.

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