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Math Help - Convergeance of Improper Integral

  1. #1
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    Convergeance of Improper Integral

    The problem statement is:
    Let of be defined on (0,1] by f(x)=d/dx(x2sin(1/x)=2xsin(1/x^2)-(2/x)cos(1/x^2)

    Show the improper Riemann Integral of f on (0,1] converges, but that the improper integral of |f| diverges on (0,1].

    I went through and solved the integral as an integral from c to 1, then took the limit as c approaches 0 for this function. For both I have found a number that they limit goes to as it approaches 0. I'm having trouble showing that the limit as |f|-> 0 diverges. I went through the same process with |f| as I did with f. Is there maybe a trick to this other than straight solving it?
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  2. #2
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    Re: Convergeance of Improper Integral

    Hey renolovexoxo.

    Can you show us what you did?
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  3. #3
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    Re: Convergeance of Improper Integral

    I evaluated
    lim c->0+ of (x^2*sin(1/x)) and then did the same for |f| by using the absolute value of the same function.
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