Let R be the region bounded by the curve y = 5 x + 1 and th

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Let R be the region bounded by the curve y = 5 x + 1 and the x-axis… Let R be the region bounded by the curve y = 5 x + 1 and the x-axis on the interval [100,8[. The graph of y = 5 /x + 1 is given here: (a) The area of ??R corresponds to the following improper integral: 8 100 (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. Math Calculus MAT 1722

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