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.
for p > 1
This integral is badly behaved at x = 0. We worked out the antiderivative of in another problem.
Since the quantity p – 1 is positive, as b approaches 0 the quantity bp – 1 will also approach 0. Then the fraction
will approach ∞. The limit does not exist, so the integral