Arkansas Tech UniversityMATH 2924: Calculus IIDr. Marcel B. FinanSolutions to Assignment 6.6Exercise 1(a) This is an improper integral of type 2 where the integrand is discontin-uous atx= 1.(b) This is an improper integral of type 1 where the interval of integrationis unbounded.(c) This is an improper integral of type 1 where the interval of integrationis unbounded.(d) This is an improper integral of type 2 where the integrand is discontin-uous atx= 0Exercise 5First, lettingu=x-2,we findZdx(x-2)32=Zu-32du=-2√u=-2√x-2+C.Thus,Z∞3dx(x-2)32= limb→∞2-2√b-2= 2so that the improper integral is convergentExercise 7First, lettingu= 3-4x,we findZdx3-4x=-14Zduu=-14ln|u|=-14ln|3-4x|+C.Thus,Z0-∞dx3-4x=lima→-∞-ln 34+14ln|3-4a|=∞so that the improper integral is divvergent1