Is the integral 1 ∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1? 0
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Originally Posted by miimi Is the integral 1 ∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1? 0 Well, $\displaystyle \sin(x)\underset{x\to 0}{\sim}x$. So your integral behaves like $\displaystyle \int_0^1\frac{dx}{x^{s-1}}$
So it is absolutely convergent if s<1, conditionally convergent if s=1 and divergent if s>1?
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