Math 1272: Calculus II
7.8 Improper integrals
Instructor: Jeff Calder
Office: 538 Vincent
Email:
http://www-users.math.umn.edu/~jwcalder/1272S19
,Infinite intervals
Rt
If a f (x) dx exists for all t > a, then we define
Z ∞ Z t
f (x) dx = lim f (x) dx
a t→∞ a
provided this limit exists. The improper integral is called convergent if the
corresponding limit exists and divergent otherwise.
R∞
Example 1. Compute 1 x12 dx.
,
,
7.8 Improper integrals
Instructor: Jeff Calder
Office: 538 Vincent
Email:
http://www-users.math.umn.edu/~jwcalder/1272S19
,Infinite intervals
Rt
If a f (x) dx exists for all t > a, then we define
Z ∞ Z t
f (x) dx = lim f (x) dx
a t→∞ a
provided this limit exists. The improper integral is called convergent if the
corresponding limit exists and divergent otherwise.
R∞
Example 1. Compute 1 x12 dx.
,
,
