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Math Help - Volumes of Integration (Tricky Problem involving both an x and y value)

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    Volumes of Integration (Tricky Problem involving both an x and y value)

    I can't seem to get this. Can someone please show me how one would go about solving this?

    Find the volume of the solid obtained by rotating the region bounded by the x- axis, the line y = 1, the curve y = ln(x), and the line x = 1/2 about the y-axis.

    Thanks.
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    Re: Volumes of Integration (Tricky Problem involving both an x and y value)

    washers
    with dy and y=0 to y=1
    outer radius is the logarithm, the inner is .5.
    I haven't done one of these in over 10 years.
    I think it's...

    \pi\int_0^1 \left[(e^y)^2-(.5)^2 \right]dy
    Last edited by matheagle; September 10th 2011 at 11:11 PM.
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    Re: Volumes of Integration (Tricky Problem involving both an x and y value)

    Quote Originally Posted by bhaktir View Post
    I can't seem to get this. Can someone please show me how one would go about solving this?

    Find the volume of the solid obtained by rotating the region bounded by the x- axis, the line y = 1, the curve y = ln(x), and the line x = 1/2 about the y-axis.

    Thanks.
    Start by sketching the region that is to be rotated. You'll see that this will be easiest to solve by rotating a larger (easier) region and subtracting another easy region.
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