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Could someone verify these integrals (no text )

  1. Oct 19, 2007 #1
    Could someone verify these integrals (no text:()

    I got these integrals wrong on a quiz I just took. Looking back, I am not quite sure what I was thinking:/ But I have reworked them and would like know if I have the integrals set up properly; I don't need to evaluate them...just set them up:

    Set up the integral to find the Volume by Cylindrical Shells of the region enclosed by [tex]y=x^2[/tex] and [tex]y=x[/tex]

    rotated about:

    x-axis: [tex]V=2\pi\int_0^1y(\sqrt{y}-y)dy[/tex]

    y-axis [tex]V=2\pi\int_0^1x(x-x^2)dx[/tex]

    and the region enclosed by y=2-x, y=x^2 in the 1st quadrant rotated around x=3: [tex]V=2\pi\int_0^1(3-x)(2-x-x^2)dx[/tex]

    I know these can be simplified, but I am not concerned with that, just the concept.

    Thanks,
    Casey
     
  2. jcsd
  3. Oct 19, 2007 #2
    I would really appreciate if some one could verify these.
     
  4. Oct 19, 2007 #3
    all 3 are correct.
     
  5. Oct 19, 2007 #4
    Thanks bob. I have an Exam on Monday!

    Casey
     
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