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Integral problem

  1. Jan 8, 2012 #1
    1. The problem statement, all variables and given/known data

    yc8m.jpg


    2. Relevant equations



    3. The attempt at a solution

    Ive solved it this way:
    yc8m.jpg = [ln |x|]1-2 = ln 1 - ln 2 = -ln2

    However the solutions say the integral is divergent, therefore it should tend to +∞ or -∞

    If someone could tell me what I've done wrong I'd appreciate!
    Thanks
     
  2. jcsd
  3. Jan 8, 2012 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    You did two things wrong.

    1. Lesser problem: Your integral is incorrect. [itex]\int 1/|x|\,dx = \mathop{\mathrm{sgn}} x \, \ln |x|[/itex], not [itex]\ln |x|[/itex].

    2. Huge problem: You integrated across a singularity.


    f(x)=1/|x| is positive everywhere. How could the integral of this function from -2 to 1 possibly be negative? That you obtained a negative result when the integrand is always positive and the integration interval is in the positive direction should have been a big warning sign indicating that you did something wrong.
     
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