Consider the region S in the first quadrant that is bounded above by the curve y=x2/31, below by the x–axis, and on the left by the vertical line x=1. The region extends indefinitely to the right.
Respond to the following.
(a) Write an integral expression that represents the exact area of S. Include any limit processes that are necessary.
(b) Evaluate the integral from part (a) and determine the exact area of S.
(c) Verify the convergence or divergence of the integral you evaluated in part (b) by explicitly analyzing the behavior of the integrand near any points where it is unbounded or where the interval of integration is unbounded.