I know that for any [itex]a>0[/itex] and [itex]k,t\in\mathbb{R}[/itex], the integral [tex]\int_0^a t^k\; dt[/tex] converges if and only if [itex]k>-1[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Is it true that if [itex]k[/itex] is complex then [tex]\displaystyle \int_0^a |t^k| \; dt[/tex] converges if and only if [itex]\text{Re}(k)>-1[/itex] since if [itex]t[/itex] is real, [itex]|t^k|[/itex] does not depend on the imaginary part of [itex]k[/itex]?

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# Homework Help: Convergence of integral

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