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Math Help - Is This Right For Volume of Solids?

  1. #1
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    Is This Right For Volume of Solids?

    Let R be the shaded region bounded by the graph of y=lnx and the line y=x-2.

    Find the volume of the solid generated when R is rotated about the horizontal line y=-3.

    Is this the correct integral for the volume?

    \pi \int^{0.15859434}_{3.1461932} [{(lnx)^2-(x-2)^2}]dx
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  2. #2
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    Quote Originally Posted by summermagic View Post
    Let R be the shaded region bounded by the graph of y=lnx and the line y=x-2.

    Find the volume of the solid generated when R is rotated about the horizontal line y=-3.

    Is this the correct integral for the volume?

    \pi \int^{0.15859434}_{3.1461932} [{(lnx)^2-(x-2)^2}]dx
    <br />
=\pi \int^{0.15859434}_{3.1461932} [{(lnx+3)^2-(x-2+3)^2}]dx<br />

    =\pi \int^{0.15859434}_{3.1461932} [{(lnx+3)^2-(x+1)^2}]dx<br />

    Finish it.
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