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Integrating with unknown method

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data



    If (the integral from -3 to 2)f(x)dx=-1, (the integral from -1 to 5)f(x)dx=8, and (the integral from -3 to 5) f(x)dx=6, then (the integral from -1 to 2)f(x)dx= ?





    2. Relevant equations

    This is the part I'm struggling with.


    3. The attempt at a solution
    I know that the answer is as follows:

    Note that (the integral from -3 to -1) f(x)dx= (the integral from -3 to 5)f(x)dx- (the integral from -1 to 5) f(x)dx= 6-8= -2. So (the integral from -1 to 2) f(x)dx= (the integral from -3 to 2) f(x)dx- (the integral from -3 to -1) f(x)dx= -1-(-2)= 1

    I just don't understand what rule allows you to do the above.
     
  2. jcsd
  3. Dec 14, 2011 #2

    SammyS

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    How does the integral from -3 to -1 plus the integral from -1 to 2 plus the integral from 2 to 5 , compare to the integral from -3 to 5 ?
     
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