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Math Help - Area between curves

  1. #1
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    Area between curves

    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?
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  2. #2
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    shells
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  3. #3
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    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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