Calculus 2 (Math-UA-122) — Fall 2018HW 4 — Section 6.6,7.1 — Improper integrals, areas (??? points)Due: Submit online (single PDF file) by 10/1/2018 before beginning of classShow all work and write clearly and neatly in order to receive full credit. If you only write the answer withno work you will not be given any credit.Improper integrals(80 points)1. (28 points) Evaluate the following integrals, and determine whether they converge or diverge. In theinstances that you are unable to evaluate the antiderivative, use the comparison test to determinewhether the integrals converge or diverge.(a)(7 points)Z∞21x2-1dx(b) (7 points)Z∞21(x3-3)1/4dx(c) (7 points)Z2-21√4-x2dx(d) (7 points)Z∞11√1 +x7dx2. (14 points) For what values ofpdo the following integrals converge?(a)(7 points)Ze11x(lnx)pdx(b) (7 points)Z∞e1x(lnx)pdx3. (20 points) For any real numbera, define a function Γ(a) (called the “gamma function”) using theimproper integral:Γ(a) =Z∞0xa-1e-xdx(Note that for most values ofait is not possible to express this integral using elementary functions.