Math 2924 Improper Integrals - Arkansas Tech University...

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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=-2u=-2x-2+C.Thus,Z3dx(x-2)32= limb→∞2-2b-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
Exercise 13First, lettingu=x2,we findZxe-x2dx=12Ze-udu=-12e-u=-12e-x2+C.

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