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Improper Integrals with Limit

  1. Oct 23, 2015 #1
    1. The problem statement, all variables and given/known data
    Evaluating the following formula: upload_2015-10-23_22-41-31.png


    3. The attempt at a solution
    Since the integral part is unknown, dividing the case into two: converging and diverging
    If converging: the overall value will always be 0
    If diverging: ...?
     
  2. jcsd
  3. Oct 23, 2015 #2
    As you say, if the integral converges for ##x \to 0^+##, the result is always zero. However, even if the integral diverges, it is still possible that one can get a finite value. This depends on the speed of divergence. Try it out with ##f(t) = 1## and ##f(t) = 1/t##. What happens for ##f(t) = 1/t^\alpha, \alpha > 1##?
     
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