Math 104: Improper Integrals (With Solutions)

Math 104: Improper Integrals (With Solutions)

Ryan Blair

University of Pennsylvania

Tuesday March 12, 2013

Ryan Blair (U Penn)

Math 104: Improper Integrals

Tuesday March 12, 2013 1 / 15

Outline

1 Improper Integrals

Ryan Blair (U Penn)

Math 104: Improper Integrals

Tuesday March 12, 2013 2 / 15

Improper Integrals

Improper integrals

b

Definite integrals f (x)dx were required to have

a

finite domain of integration [a, b] finite integrand f (x) < ?

Ryan Blair (U Penn)

Math 104: Improper Integrals

Tuesday March 12, 2013 3 / 15

Improper Integrals

Improper integrals

b

Definite integrals f (x)dx were required to have

a

finite domain of integration [a, b] finite integrand f (x) < ?

Improper integrals 1 Infinite limits of integration 2 Integrals with vertical asymptotes i.e. with infinite discontinuity

Ryan Blair (U Penn)

Math 104: Improper Integrals

Tuesday March 12, 2013 3 / 15

Improper Integrals

Infinite limits of integration

Definition Improper integrals are said to be

convergent if the limit is finite and that limit is the value of the improper integral. divergent if the limit does not exist.

Ryan Blair (U Penn)

Math 104: Improper Integrals

Tuesday March 12, 2013 4 / 15

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