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Math Help - solids of revolution/integration question

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    solids of revolution/integration question

    The volume of the solid formed when the region bounded by the curve y = e^x - k , the x-axis and the line x=ln3 is rotated about the x-axis is pi*ln3 units cubed. Find k.
    Last edited by shawli; January 4th 2010 at 05:54 PM.
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    Quote Originally Posted by shawli View Post
    The volume of the solid formed when the region bounded by the curve , the x-axis and the line x=ln3 is rotated about the x-axis is pi*ln3 units cubed. Find k.
    please confirm ...

    is the function y = e^{x-k} or y = e^x - k ?
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    Quote Originally Posted by skeeter View Post
    please confirm ...

    is the function y = e^{x-k} or y = e^x - k ?
    The second one, y = e^x - k.
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    Quote Originally Posted by shawli View Post
    The second one, y = e^x - k.
    any other information about the constant k ?
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    Nope, that is the question exactly as it is given. I could post the answer at the back of the text book if you'd like to verify your solution though?
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    Quote Originally Posted by shawli View Post
    The volume of the solid formed when the region bounded by the curve y = e^x - k , the x-axis and the line x=ln3 is rotated about the x-axis is pi*ln3 units cubed. Find k.
    Solve \int_{\ln k}^{\ln 3} (e^x - k)^2 \, dx = \ln 3 for k. I get k = 1.
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