Example IMPROPER INTEGRALS Improper Integral TYPE-I: Infinite Limits of Integration TYPE-I: Infinite Limits of Integration Example TYPE-II: Discontinuous.
Post on 18-Jan-2018
301 Views
Preview:
DESCRIPTION
Transcript
Example
IMPROPER INTEGRALS
Improper Integral
TYPE-I:Infinite Limits of Integration
1 2 1 dxx
Example
1
1 2 1 dxx
TYPE-II:Discontinuous IntegrandIntegrands with Vertical
Asymptotes
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
b
aba dxxf dxxf )(lim)(
Example
1 2 1 dxx
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
b
aa
b dxxf dxxf )(lim)(
Example
0 dxxex
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
b
aa
b dxxf dxxf )(lim)(
b
aba dxxf dxxf )(lim)(
The improper integrals
are called convergent if the corresponding limit exists and divergent if the limit does not exist.
a dxxf )(
a dxxf )(
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
t
ata dxxf dxxf )(lim)(
Example
1 1 dx
x
IMPROPER INTEGRALS
082
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 1
dxxf )(
If both improper integrals
are convergent
a dxxf )(
a dxxf )(
convergent
dxxf )(
a
a dxxf dxxf )()(
Example
dx
x 11
2
Memorize:
IMPROPER INTEGRALS
Example
IMPROPER INTEGRALS
Improper Integral
TYPE-I:Infinite Limits of Integration
1 2 1 dxx
Example
1
1 2 1 dxx
TYPE-II:Discontinuous IntegrandIntegrands with Vertical
Asymptotes
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
5
2
21 dx
x
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
2/
0 sec
dxx
Example
1
0
11 dx
x
IMPROPER INTEGRALS
DEFINITION OF AN IMPROPER INTEGRAL OF TYPE 2
Example
3
0 11 dxx
IMPROPER INTEGRALS
F092
IMPROPER INTEGRALS
Example
1
0 ln dxx
IMPROPER INTEGRALS
IMPROPER INTEGRALS
IMPROPER INTEGRALS
F112
IMPROPER INTEGRALS
IMPROPER INTEGRALS
F092
IMPROPER INTEGRALS
F102
top related