# Improper Integrals with Limit

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1. Oct 23, 2015

### JIHUN

1. The problem statement, all variables and given/known data
Evaluating the following formula:

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. Oct 23, 2015

### Sir Beaver

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 $f(t) = 1/t^\alpha, \alpha > 1$?