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Area between 2 curves

  1. Feb 3, 2006 #1
    I know how to do this graphically, but I can't remember how to set it up the long way. The equations are:

    y^2=x and y=x-2

    I know it should be easy, but it's late and I can't think...
  2. jcsd
  3. Feb 3, 2006 #2
    Find the intersection points then set up the integral from the one intersection point to the other of the "larger" curve minus the "smaller" curve.
  4. Feb 3, 2006 #3


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    Homework Helper

    Solve for the points of intersection of the two curves:


    and [tex]y=x-2 \Rightarrow x=y+2[/tex]

    the intersection of these curves occurs at the values of y such that

    [tex]y^2=y+2 \Rightarrow y^2-y-2=(y+1)(y-2)=0[/tex]

    so [tex]y=-1,2[/tex] and recall that [tex]x=y+2[/tex],

    so the points are: (1,-1) & (4,2)

    The integrand is easiest as: rightmost curve - leftmost curve = [tex](y+2) - y^2[/tex]

    and the integral is then [tex]\int_{y=-1}^{2} (y+2-y^2)dy[/tex]
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