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Volume by revolution

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data
    let R be the region enclosed by the x-axis,y-axis and the curve y=cos(x^2)
    A)find the exact volume of the solid of revolution obtained by rotating R about the y-axis

    B) find the exact volume of the solid of revolution obtained by rotating R about the x-axis

    i am lost on the integration limit and how to set up this problem help please got exam in 10hours
    2. Relevant equations

    3. The attempt at a solution
    A) r=X and h= cos(x^2)
    so integrate from 0 to infinity of 2 pi (x)(cos(x^2)) dx= pi sin(x^2)<-i dont think this is correct
  2. jcsd
  3. Apr 20, 2010 #2


    Staff: Mentor

    Is this the exact description of the region as shown in your book? A better description might be "the region in the first quadrant enclosed by the x-axis,y-axis and the curve y=cos(x^2)."
    Where does the graph of y = cos(x^2) cross each axis? For the first problem, are you using cylindrical shells or disks? Same for the second problem. I can tell which method you are using, but you should say what method you're using as part of the work you do.

    For each integral, what's the volume of your typical volume element? That will correspond directly to your integrand.
  4. Apr 20, 2010 #3
    thanks a lot man it makes more sense now
    ps: this question was from a previous exam i was not given any grap or any thing

    i got it now thanks again
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