I'm having trouble determining if this integral is convergent or not:
If I graph the integrand, it appears that for
So I attempted the comparison theorem:
This is divergent right? So this was useless??
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split it into two sets, one for and the other one for so for each is and the integral converges.
I understand everything except the point of writing:
Why split the interval?
i could've picked any number there, but to make my life easier i took a "one."
besides, one doesn't care about the first piece, since is a continuous function being integrated over a compact set.
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