Evaluate the following: integral -infinity to +infinity xe^-x^2 dx.
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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.
`int_(-oo)^(oo)e^(-x^2)xdx=0`
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...
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