For what real values of x does the integral converge? Prove your answer.
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Since $\displaystyle t^{x-1}e^{-t}\leq{e^{\frac{-t}{2}}}$ and $\displaystyle \int_{0}^{\infty}e^{\frac{-t}{2}}dt$ is convergent, then it is absolutely convergent for $\displaystyle x\geq{1}$
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