Science:Math Exam Resources/Courses/MATH101/April 2016/Question 02 (d)/Solution 1

Since $x{e}^{x^2}$ is an odd function, i.e.,

$f(x)=x{e}^{x^2}=-(-x)e^{(-x{)}^2}=-f(-x)$,

we have $\underset{-2}{\overset{2}{\int }}x{e}^{x^2}dx=0$.