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Volumes of Solids of Revolution

  1. Feb 11, 2014 #1
    Question


    I'm really having issues grasping the Volumes of Solids of revolution. I could use some help solving this question, it isn't very hard.

    1. Let R be the region bounded by y = x2 and y = x + 2. Find:

    a) the area of R

    b) the volume of the solid if R is rotated about the x-axis

    c) the volume of the solid if R is rotated about the the line x = 4





    2. Relevant equations



    3. The attempt at a solution

    Basically this is what I've gotten.



    a)
    Area = ∫((x+2)-(x2))dx
    = (x2/2 + 2x) - (x3/3), evaluated over the interval (-1,2)
    = 4.5


    b) this is what I did but I don't know if it is right

    ∏∫((x+2)2 - (x2))dx
    = ∏∫((x2+4x+4) - x4) dx
    = ∏(x5/5 - x3/3 -2x2 -4x) evaluated from (-1,2)
    = 72∏/5

    c) I'm not sure how to start this one.
     
  2. jcsd
  3. Feb 11, 2014 #2
    a and b look right. For c, have you learned the shell method for integration?
     
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