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Easy integral what am i doing wrong?

  1. Jun 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Integral[ x - 2|x|]dx from [-1,2]


    3. The attempt at a solution

    Wouldn't it become x^2/2 - 2x^2/2 so x^2/2 - x^2 and then -x^2/2?

    So from [-1,2] it would just be

    -((2^2)/2) - - ((-1)^2/2) which is -1.5 but the answer is -3.5.....
     
  2. jcsd
  3. Jun 12, 2010 #2
  4. Jun 12, 2010 #3
    Wait, sorry this shouldnt be the issue because from my graph the whole function is negative anyway... any suggestions?
     
  5. Jun 12, 2010 #4

    Borek

    User Avatar

    Staff: Mentor

    I can be wrong, but I would try

    [tex]\int_{-1}^2f(x)dx = \int_{-1}^0f(x)dx + \int_{0}^2f(x)dx[/tex]
     
  6. Jun 12, 2010 #5

    Mark44

    Staff: Mentor

    I agree with Borek. The idea is that you can eliminate the absolute values by looking at the integrand on [-1, 0] and on [0, 2].

    If x <= 0, |x| = -x.
    If x >= 0, |x| = x.
     
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