Question

\[\int_{\infty}^{-\infty} xe^{-x^2} dx\]
=
\[\int_{\infty}^{0} xe^{-x^2} dx +\int_{0}^{-infty} xe^{-x^2} dx\]
=\[\lim_{t \rightarrow \infty} \int_{t}^{0} xe^{-x^2} dx\]
=

Answer 1

=\[-\frac 1 2 \]

Answer 2

and the other one is \[\frac 1 2 \]
?