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What am I doing wrong integrating with 1-|x|?

  1. Jan 20, 2014 #1
    I understand [itex]\int[/itex][itex]^{1}_{-1}[/itex]1-|x|dx = 1 visually just by graphing it and taking the area of the triangle but for the sake of more complicated examples I'm not exactly sure what step I'm messing up when I use the FTOC:

    |x|= x when x>0, -x when x<0

    [itex]\int[/itex][itex]^{0}_{-1}[/itex]1-|x|dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-|x|dx


    = [itex]\int[/itex][itex]^{0}_{-1}[/itex]1-(-x)dx + [itex]\int[/itex][itex]^{1}_{0}[/itex]1-(x)dx


    = [itex]\frac{x^2}{2}[/itex]|[itex]^{0}_{-1}[/itex] - [itex]\frac{x^2}{2}[/itex]|[itex]^{1}_{0}[/itex]

    = -1/2 - 1/2 = -1 [itex]\neq[/itex]1

    Any input is appreciated and hope this makes sense lol (still getting used to the formula drawer).
     
  2. jcsd
  3. Jan 20, 2014 #2

    tiny-tim

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    hi zmalone! welcome to pf! :smile:
    you missed out [x]-11, = 2 :wink:
     
  4. Jan 20, 2014 #3
    Wow :( I don't know why I was taking the derivative of 1 instead its anti-derivative but I certainly confused myself by doing so for the past half hour. Thanks for pointing it out!
     
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