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Math Help - Solid & revolution help

  1. #1
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    Solid & revolution help

    Let R be the region enclosed by the graphs of y = 2lnx and y = x/2 and the lines x = 2 and x = 8. Set up an integral expressing the volume of the solid generated when R is revolved about the line x = -1.

    A correct answer is 2pi{(x+1)(2lnx - x/2)dx (limits from x=0 to x=8)

    But what about in terms of dy? I tried to set up an integral but my calculator says it's different from the above expression.

    pi{(2y+1)-(e^(y/2) + 1)dx (limits from y=1 to y=2ln8)

    What's up?
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  2. #2
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    Nvm, I got it. It turns out you can't use the dy method because you can't accurately capture the region since it's bounded by vertical lines (dy denotes horizontal lines). I think...
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