Question

(a) Set up the appropriate limit(s) to evaluate the improper integral Do not evaluate the limit(s). = dr. (6) Determine whether the following integrals is proper, improper and convergent, or improper and divergent. Justify your answer. *1 + arctan(1) 10 (c) Evaluate the following integral or determine whether it is convergent.

Answer 1

دام 4 x²-3x Cor 1 it 4 بطل = t> 0 x 23 x dx t dx - lim 4 (x-3) x t∞ t Elm 461 2 da t70o31 (x-3 t = 4 lim ln (2-3 3 too x In 2 = 4 lim og In It 3 37²0 t 17 4 In (1) - In (2) 3 =-4 In 2 3.

dr Llxt arc tun (x) 7 i ) 5xotx as limits are not finite so it ind improper integral By limit test are tan(x) + x lim X-70 Srb ta 1 are tan(R) lim X>0 23 x2 1+1/x5 O - lom So it is convergent