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Evaluating integrals

  1. May 13, 2013 #1
    1. The problem statement, all variables and given/known data


    Given
    7 f(x) dx= 8
    0

    7 f(x) dx = −3
    1

    evaluate the following.

    1 f(x) dx
    0



    2. Relevant equations
    n/a


    3. The attempt at a solution

    I'm a little confused on how to approach this problem. Do i use the additive interval property of integrals?
     
  2. jcsd
  3. May 13, 2013 #2

    Mark44

    Staff: Mentor

    Yes.
     
  4. May 13, 2013 #3
    I ended up with 5. Is that correct?
     
    Last edited: May 13, 2013
  5. May 13, 2013 #4

    Mark44

    Staff: Mentor

    So 5 + (-3) = 8?
     
  6. May 13, 2013 #5

    UVW

    User Avatar

    To expand on what Mark44 is saying, remember that these integrals represent areas under your curve, f(x). If you know how much area is under the curve between x = 0 and x = 7 and also know how much area is under the curve between x = 1 and x = 7, can you intuitively decide how to find the area between x = 0 and x = 1?
     
  7. May 13, 2013 #6
    Yea I understand but when I use the formula i keep getting 5. I don't see where I'm going wrong.
     
  8. May 13, 2013 #7
    [itex] \int_0^7 f(x) dx = \int_0^1 f(x) dx + \int_1^7 f(x) dx [/itex]. What happens when you plug in what you know?
     
  9. May 13, 2013 #8
    I calculated 11 using that formula.
     
  10. May 13, 2013 #9
    Good, that's right.
     
  11. May 13, 2013 #10
    Thanks
     
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