Class Notes (1,100,000)

US (460,000)

UC-Irvine (10,000)

MATH (1,000)

MATH 2B (600)

ERJAEE, G. (20)

Lecture 17

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

17This

**preview**shows half of the first page. to view the full**3 pages of the document.**02/13/2019

MATH 2B - Lecture 17 - Improper Integrals

We know the definite integral usually has a function f(x) that is defined on a finite

interval [a,b]. Now we generalize the concept by considering two cases:

1. Infinite Intervals

2. Discontinuous Integrands

Infinite Intervals

Example:

● Consider the region bounded by

, on the interval [1,t]

F.T.C Part II

● We note that

is always less

than 1

● If we take

, we have

● This tells us that, in the case of

, the region s has infinite length, but the area

of this region is finite

● This is the first type of improper integral

a) If

exists for every number , then

b) If

exists for every number , then

● If the improper integrals exists and gives us a finite number, then

we say the improper integral is convergent, otherwise it is divergent

c) If

and

are convergent, then we can define

###### You're Reading a Preview

Unlock to view full version

Subscribers Only