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Math Help - Convergence of an integral

  1. #1
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    Convergence of an integral

    Is the integral
    1
    ∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1?
    0
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by miimi View Post
    Is the integral
    1
    ∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1?
    0
    Well, \sin(x)\underset{x\to 0}{\sim}x. So your integral behaves like \int_0^1\frac{dx}{x^{s-1}}
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  3. #3
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    So it is absolutely convergent if s<1, conditionally convergent if s=1 and divergent if s>1?
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