Answer
0
Work Step by Step
$f(x)=x*e^{-x^2}$ is an odd function because $f(-x)=-f(x)$. This means that it is symmetric with respect to the origin. Thus, we know that:
$\int ^\infty _0 x*e^{-x^2}dx $ = -$\int ^0 _-\infty *e^{-x^2}dx $
Therefore, the answer is 0.
