Question

Evaluate the integral of xe^(-x^2) dx from 0 to infinity and state whether it is convergent or divergent.

Answer 1

will not always be possible to evaluate improper ... in whether the integral is convergent or divergent. .... area under the smaller function is infinite (i.e. ∫∞ag(x)dx ...

Answer 2

x dx divergent (p-test). 2. ∫ ∞. 1 e−x dx convergent (integrate) ... xe−x dx convergent (integrate by parts) ... If ∫ f is convergent and 0 ≤ g(x) ≤ f(x) for all x ...