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Math Help - Volume of solid of revolution

  1. #1
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    Volume of solid of revolution

    Let R be the region in Quadrant 1 bounded by the graphs of y=lnx and y=1.Find the exact volume of the solid generated by rotating R about the y-axis.

    Thanks for help.
    Last edited by mr fantastic; March 13th 2010 at 04:43 PM. Reason: Changed post title
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    MHF Contributor chisigma's Avatar
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    The requested volume is...

    V= \pi\cdot \int_{0}^{1} e^{2x}\cdot dx = \frac{\pi}{2}\cdot (e^{2}-1) (1)

    Kind regards

    \chi \sigma
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  3. #3
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    thank you,could you tell me where did you get that e^2x?
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  4. #4
    Member TheMasterMind's Avatar
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    Quote Originally Posted by jupiter92 View Post
    Let R be the region in Quadrant 1 bounded by the graphs of y=lnx and y=1.Find the exact volume of the solid generated by rotating R about the y-axis.

    Thanks for help.
    A=circumference x height= 2\pi x(1-ln x)

    dV= 2\pi x (1- ln x) dx

    <br />
\int^{e}_{1} 2\pi x (1- ln x) dx

    now integrate
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  5. #5
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by jupiter92 View Post
    thank you,could you tell me where did you get that e^2x?
    Simply I swap the y-axis and the x-axis so that the area is defined for 0\le x \le 1 and 1\le y \le e^{x} and rotation is around the x axis. This conducts to use the formula...

    V= \pi\cdot \int_{0}^{1} f^{2}(x)\cdot dx (1)

    ... where f(x)= e^{x}, formula that leads to a more confortable integration...

    Kind regards

    \chi \sigma
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  6. #6
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    thanks.
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  7. #7
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    btw,could you tell me what does the dx stand for?
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