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Trouble finding the integral for volume

  1. Feb 3, 2005 #1
    I'm having trouble finding the integral I'm supposed to use for some Volume problems...
    Can someone lead me in the direction as to how I should form my integrals to get the solutions?
    The below is a scanned page from an AP Calculus textbook, I'm pretty much stumped on how to solve 56-59..
    Hope someone can help.

  2. jcsd
  3. Feb 3, 2005 #2
    I'll give you some hints on the first one (56a). They're all pretty much the same. The side of the squares are determined by the difference between the two functions y=x+1 and y=x^2-1. This difference is x-x^2+2, it is zero for x=-1 and x=2. So now you have determined the shape of your base.

    With this you can easily find the area of such a square. Integrating over x gives you the total volume.
  4. Feb 3, 2005 #3
    OK, so you merely evaluate the integral [tex]A (x) = \int_{-1}^\2 2 x - x^{2} + 2 dx[/tex]?
    Does anybody have a clue about the other questions?
    Last edited: Feb 3, 2005
  5. Feb 4, 2005 #4
    Well, if you want to evalute the area enclosed by the two lines (y=..) yes, but...
  6. Feb 4, 2005 #5


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    [itex]x - x^2+2[/itex] gives the length of one side of the square as a function of x. You need the area of the square.

    b) Is somewhat easier, since the height of each rectangle is one, that means the area of a cross sectional rectangle is [itex]x-x^2+2[/itex].
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