Comparison Theorem

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• August 25th 2010, 02:08 PM
SyNtHeSiS
Comparison Theorem
Use the Comparison Theorem to determine whether the integral is convergent/divergent: $\int_{0}^{1} \frac{sec^{2}x}{x\sqrt{x}} dx$

I dont know which basic function to compare it to. I tried comparing it to 1/x but that didnt work out.
• August 25th 2010, 02:48 PM
Ackbeet
The secant function is bounded on the interval, so the convergence doesn't depend on that function. Close to zero, the numerator looks like 1. So I would compare the integrand to the function $x^{-3/2}.$