Calculus 221, section 9.6b Improper Integrals, part 2
Notes prepared by Tim Pilachowski
We continue working with improper integrals, moving beyond antiderivatives to integration by substitution and
integration by parts. Recall the basic process:
() ()
∫∫ ∞→
∞
=b
a
b
adxxfdxxf lim . When the limit goes to a
particular number value, the improper integral is convergent. Otherwise, the improper integral is divergent.
Example N. ∫∞
−
322
dx
x
x answer: divergent
Example O.
()
∫∞
−
32
22
dx
x
x answer: converges to 14
1
Example P. answer: converges to
∫∞−
0
2dx
x
xe 4
1
