Determine whether the integral converges or diverges. Indicate on a graph the region whose weighted area is given by the integral. If the integral converges, find its value.
This function is badly behaved at the upper limit of integration x = 0. We write the improper integral as a limit, work out the integral, then evaluate the limit.
This integral diverges, since approaches ∞ as b approaches 0. That means the area of this region is infinite.