Find the area between the graph of f(x)= x(e^-x^2) and the x-axis for the interval (0, ∞). Your work must include the proper notation and show the antiderivative. If the integral diverges, show why.

Answer 1

∫xe^(-x^2) dx = -1/2 e^(-x^2)
so, integrating from 0 to ∞, that is
-1/2 [ lim(x->∞) e^(-x^2) - 1] = -1/2 [0 - 1] = 1/2