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Math Help - Perpendicular Cross Section

  1. #1
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    Perpendicular Cross Section

    i completely forgot how to do these type of problems:

    the base of a solid is the region bounded by y=e^(-x), the x-axis, the y-axis, and the line x=1. each cross section perpendicular to the x-axis is a square. find the volume of the solid and keep your answer in terms of e
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  2. #2
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    the cross-sectional area is A(x) = (e^{-x})^2

    V = \int_0^1 (e^{-x})^2 \, dx

    V = \left[-\frac{1}{2}e^{-2x}\right]_0^1 = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]
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