Use the comparison Theorem to determine whether the integral is convergent or divergent integral from 0,1 [e^(-x)]/sqrt(x) thanks guys
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Originally Posted by Asuhuman18 Use the comparison Theorem to determine whether the integral is convergent or divergent integral from 0,1 [e^(-x)]/sqrt(x) thanks guys . and it is easy to show that the improper integral converges. Hence, your improper integral converges. T
Last edited by Ted; Feb 20th 2010 at 07:10 AM.
or for and in particular for holds and verifies the convergence of the original integral.
Similar to what Krizalid has shown, we can also find a lower bound. For all , we have , which yields by integrating after dividing by Note that above, we apply improper integration and that provided that .
Last edited by bkarpuz; Feb 20th 2010 at 07:24 AM. Reason: Ted pointed out a correction.
Originally Posted by bkarpuz Similar to what Krizalid has shown, we can also find a lower bound. For all , we have , which yields by integrating Recall that It should be .
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