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 x = 0, which is the lower limit of integration. We write out the improper integral as the limit it is, then evaluate:
As b approaches 0, the quantity b.6 also approaches 0. So the integral converges to .