Convergence integrals
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Leave a comment if you need any clarifications.

@Phia: What details do you need?

I added some more detail. Let me know if you need any clarifications, but the solution is pretty much what I have written.

Can you explain why the integral converges if the lim is 0?

I am not saying that he integral converges if the lim is 0. If the limit is not zero then the integral is divergent. This is a well known fact about improper integrals which can be easily found in any calculus textbook.
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