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Math Help - Integral-volume by Cylindrical shells

  1. #1
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    Integral-volume by Cylindrical shells

    Hi, I need help with regards to whether or not I've set this up correctly . The question asks," use the method of cylindrical shells to find the volume.... bounded by the given curves

    y=e^x, x=0, and y=pi about the X-axis


    V=2(pi)rh dy

    Interval=1 to pi
    radius =y-1
    height = ln (y) by solving y=e^x for x=ln y
    thickness = dy

    So V= ∫[1,pi] 2pi(y-1)(ln(y)) dy

    Is this correct? I'm not sure on the radius....
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  2. #2
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    radius = y

    h = ln(y)

    V = 2\pi \int_1^{\pi} y \cdot \ln(y) \, dy \approx 21.561

    confirm using washers ...

    V = \pi \int_0^{\ln(\pi)} \pi^2 - e^{2x} \, dx \approx 21.561
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