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Math Help - volume

  1. #1
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    integral

    volume-slide1.jpg
    y=sqrt(x+1),x=1,y=-1
    i have to find a volume(certain integral) of geometric body which is showed (produced) by y=sqrt(x+1) rotation about y=-1...
    Last edited by mathe26; March 19th 2013 at 01:27 PM.
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  2. #2
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    Re: volume

    For each x, the point (x, \sqrt{x+1}), rotated around the axis y= -1, moves in a circle with center at (x, -1) and radius \sqrt{x+ 1}- (-1)= \sqrt{x+1}+ 1. That circle has area \pi r^2= \pi (\sqrt{x+1}+ 1)^2. Thinking of that as a very thin disk with thickness "dx", its volume is \pi (\sqrt{x+1}+ 1)^2 dx. The total volume is the "sum" of all those disks: \pi\int_{-1}^1(\sqrt{x+1}+1)^2 dx.
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