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Math Help - Volume about y axis

  1. #1
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    Volume about y axis

    Find the volume of the solid formed by rotating the region enclosed by
    , \ , \ , \
    about the y-axis.

    I'm just at a loss here as to how to proceed. It's a change about the y axis so I assume the functions have to be done with respect to y, but how can that be done for the first one, y = e^x + 1?

    Any help on how to begin would be appreciated.
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    Find the volume of the solid formed by rotating the region enclosed by
    , \ , \ , \
    about the y-axis.

    I'm just at a loss here as to how to proceed. It's a change about the y axis so I assume the functions have to be done with respect to y, but how can that be done for the first one, y = e^x + 1?

    Any help on how to begin would be appreciated.
    use the method of cylindrical shells w/r to x ...

    V = 2\pi \int_0^{0.9} x(e^x + 1) \, dx

    ... or use two integral expressions w/r to y.

    V = \pi \int_0^2 (0.9)^2 \, dx + \int_2^{e^{0.9}+1} (0.9)^2 - [\ln(y-1)]^2 \, dy
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    Quote Originally Posted by skeeter View Post
    use the method of cylindrical shells w/r to x ...

    V = 2\pi \int_0^{0.9} x(e^x + 1) \, dx

    ... or use two integral expressions w/r to y.

    V = \pi \int_0^2 (0.9)^2 \, dx + \int_2^{e^{0.9}+1} (0.9)^2 - [\ln(y-1)]^2 \, dy
    Thank you. I think there was a way to find the integral of x(e^x+1) by using substitution ... is this true, and how?
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  4. #4
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    Quote Originally Posted by Archduke01 View Post
    Thank you. I think there was a way to find the integral of x(e^x+1) by using substitution ... is this true, and how?
    you would need to use the method of integration by parts.
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