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Math Help - Volume by cylindrical shells

  1. #1
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    Volume by cylindrical shells

    Just got back from my universities free tutoring sessions, and i think I have a pretty good grasp on this whole volume by cylindrical shells, (and pretty much every other shape). However I want to make sure I am doing these practice problems correctly so I don't get into a bad habit.

    The problem is:

    Consider the shape created by the lines y=31e^x , y=31e^(-x) , and x=1 revolved about the y-axis.

    So what i setup was:
    INTEGRAL of: (2pi)(r)(h)(dx)
    I set r = 31e^x
    h = 31e^x - 31e^(-x)
    and then dx for the thickness

    After you distribute terms i got INTEGRAL of: 2pi*31e^(x^2)

    I pulled the 31 and 2pi out to get
    62pi * INTEGRAL of: e^(x^2)
    I solved for the integral and got e^(x^2)*(1/2x)
    I evaluated that integral from 0-1 and got .5e
    So my final answer was 31pi

    On a side note, i have been looking for a 'how to' on how to use the math tags so i can make my expressions look all neat and what not, but can't seem to find it. I looked around different stickies, the faq, and the mathhelpwiki.

    Thanks in advance to anyone who helps!
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  2. #2
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    radius of a representative cylindrical shell is x, not 31e^x.

    V = 2\pi \int_0^1 x(31e^x - 31e^{-x}) \, dx
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