Determine whether $\displaystyle \int_{-\infty}^{\infty} xe^{-x^2}dx$ is convergent or divergent. Evaluate it if it is convergent. I tried using integration by parts, but failed to integrate $\displaystyle e^{-x^2}$.

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- Aug 25th 2010, 01:56 PMSyNtHeSiSImproper integral (convergent/divergent)
Determine whether $\displaystyle \int_{-\infty}^{\infty} xe^{-x^2}dx$ is convergent or divergent. Evaluate it if it is convergent. I tried using integration by parts, but failed to integrate $\displaystyle e^{-x^2}$.

- Aug 25th 2010, 02:09 PMDefunkt
You don't need integration by parts.

The substitution $\displaystyle u=x^2$ will easily solve this. - Aug 25th 2010, 03:47 PMTed
Its = 0

unless the lower limit is -infinity.