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Find the area between two curves.

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the area between the curves y= (7-x)/5, y = +sqrt(x+7) , y = -sqrt(x+7)


    2. Relevant equations



    3. The attempt at a solution
    I found the points of intersection of the graphs are at x=-7, x=-3 and x=42. So I know I need to do two integrals:

    One from -7 to -3, and the other from -3 to 42. But I don't know what exactly to integrate =/

    Please help!
     
    Last edited: Mar 9, 2009
  2. jcsd
  3. Mar 9, 2009 #2

    lanedance

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    Homework Helper

    Hi jumbogala, you're on the right track - try drawing a picture of you curves

    the integral for each section will be the difference of 2 curves (greater y - lesser y valued curve)

    use you picture to pick the 2 curves to use for each intergal
     
  4. Mar 9, 2009 #3
    Hmm, except that there are three curves so there's actually one on top with 2 underneath... do I have to pick just 2 curves for each integral?
     
  5. Mar 9, 2009 #4

    lanedance

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    Homework Helper

    if you sketch you curves, you will see all 3 bound a single area, the area you are trying to find

    for any given infintesimal x interval dx, only 2 curves will be acting as the bounds, so use your curve sketch to pick the correct curves for the integral
     
  6. Mar 9, 2009 #5
    okay I think I kind of get it...

    Between -7 and -3 the area is bounded by +sqrt(x+7) and -sqrt(x+7)

    Between -3 and 42 it is bounded by (x-7)/5 and -sqrt(x+7)

    Which works, so it must be the right answer. Thank you!
     
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