Let R be the region bounded by the curve y = 5 x + 1 and the x-axis on the interval [100,[. The graph of y = 5 /x + 1 is given here:

(a) The area of R corresponds to the following improper integral: 100 (5/ x + 1 dx.) Determine if this integral converges or diverges. If it converges, find its exact value. Your the answer must be well justified.

(b) Let S be the solid of revolution obtained by rotation around the x axis. Give a expression for the approximate volume V(x) of a chopped slice of S comprises between planes of abscissa x and x + x (where x is small). (

c) Find the improper integral that calculates the volume of S and determine if it converges We diverge. If it converges, find the exact value of the volume of S. Your answer should be justified. Use the appropriate mathematical notation.