How do you deal with absolute values in your Integrals?

  • Thread starter Shinjo
  • Start date
  • #1
12
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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:
 

Answers and Replies

  • #2
998
0
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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