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Math Help - integral converge or diverge

  1. #1
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    integral converge or diverge

    does this integral converge or diverge?

    a) int from 0 to infinity of e^(-x)/sqrroot(x)

    b) int from o to pi/2 of 1/sqroot(sec(x)-1))
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  2. #2
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    Krizalid's Avatar
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    For the first one, split it into two pieces: \int_{0}^{\infty }{\frac{dx}{e^{x}\sqrt{x}}}=\int_{0}^{1}{\frac{dx}  {e^{x}\sqrt{x}}}+\int_{1}^{\infty }{\frac{dx}{e^{x}\sqrt{x}}}.

    The first one converges by simple limit comparison test with \int_0^1\frac{dx}{\sqrt x}, the second one just require a simple bound to determine its convergence. I'll let you to figure out.
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