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Homework Help: Volumes of Solids of Revolutions Help!

  1. Jul 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

    y=x, y=0, x=2, x=4; about x=1

    3. The attempt at a solution
    one of the radii is x=y but im not sure how to find the other one and the interval? Please explain this one to me. Thanks!
  2. jcsd
  3. Jul 28, 2012 #2


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    Hello jzsc. Welcome to PF !

    Which are you using, the disk method or the washer method ? Until you decide that, you can't specify a radius.
  4. Jul 29, 2012 #3
    thank you SammyS! I am using the washer's method
  5. Jul 30, 2012 #4
    [itex]2\Pi\int x f(x) dx[/itex]

    The x is serving as the distance from the y-axis (the radius), so if you're rotating around x=1 rather than x=0....

    (I don't know how to put the a & b above and below the integrand)
    Last edited: Jul 30, 2012
  6. Jul 30, 2012 #5


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    [itex]2\Pi\int_a^b x f(x) dx[/itex]

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