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Absolute value definite integral

  1. Apr 9, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫[|2x-1|] evaluated on the interval [1,-1]

    2. Relevant equations



    3. The attempt at a solution

    I know we must split it into two equations ∫ from [a,c] + ∫ from [c,b]

    and in absolute value one is negative and one is positive, so it will be

    2x-1, and 1-2x my question is how do we know which interval to place each one in.

    Do we place 1-2x in the interval from [c,b] or 2x-1, and vice versa,

    thank you
     
  2. jcsd
  3. Apr 9, 2012 #2

    SammyS

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    Where is 2x-1 ≥ 0 ?

    Where is 1-2x ≥ 0 ?
     
  4. Apr 9, 2012 #3
    for 2x-1 when x is greater than or = to 1/2

    and for 1-2x when x is less than or = to 1/2

    ?
     
  5. Apr 9, 2012 #4

    SammyS

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    That should allow you to evaluate [itex]\displaystyle \int_{-1}^1\ |2x-1|\,dx\,.[/itex]
     
  6. Apr 9, 2012 #5
    Ohh so what you are saying is since 1-2x is less than 1/2 it goes in the interval from [0,1/2]?
     
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