Evaluate the following: integral -infinity to +infinity xe^-x^2 dx.
We are asked to evaluate `int_(-oo)^(oo)e^(-x^2)xdx`
I. The easy way is to recognize `xe^(-x^2)` as an odd function. ( f(-x)=-f(x) ). Since the limits of integration are symmetric about the origin, the integral is zero.
II. If you did not see that, we can apply what we know of improper integrals. Improper integrals are integrals with either or both limits at...
(The entire section contains 230 words.)
check Approved by eNotes Editorial