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 $\displaystyle e^{-x^2}$.
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 $\displaystyle e^{-x^2}$.