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How do you deal with absolute values in your Integrals?

  1. Mar 17, 2005 #1
    I have to solve the integral:

    [tex]\int^1_{-1} e^{-| |x| - \frac{1}{4} |} dx[/tex]

    but I have no idea what to do with the absolute value signs. Can someone help me? :confused:
  2. jcsd
  3. Mar 17, 2005 #2
    When is [tex]x < 0[/tex]? When is [tex]|x|-1/4 <0[/tex]? Split up the integral as is appropriate. For example,

    [tex]\int_{-5}^5 e^{|x|} \ dx = 2\int_0^5 e^x \ dx[/tex]

    [tex] \int_0^5 |x-4| \ dx = \int_0^4 4-x \ dx + \int_4^5 x-4 \ dx[/tex]
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