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Math Help - Volume of a Solid: Region Bound and Rotated about y-axis

  1. #1
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    Volume of a Solid: Region Bound and Rotated about y-axis

    The region bounded by y=e^{-x^2},\ y=0,\ x=0, and x=1 is revolved about the y-axis. Find the volume of the resulting solid.

    I know that the answer is 2\pi\int_0^1xe^{-x^2}, however I am not sure how to get there. I drew a picture, and I can't tell if I'm supposed to approximate with disks or shells...or approach it a different way. Any insight offered is appreciated. Thanks in advance.
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  2. #2
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    It looks like wherever you found the answer used the method of shells. The formula for shell integration is \displaystyle 2 \pi \int_a^b x f(x) \, dx (when the axis of revolution is the y-axis).

    According to the formula for shell integration, the volume V of the solid is given by: \displaystyle 2 \pi \int_0^1 x e^{-x^2} \, dx
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