7.8 - Improper Integration
Math 142 - Spring 2020
7.8 - Improper Integration
Goals of this section:
•
Identify and evaluate improper integrals.
f An
improper integral
is an integral that represents the (signed) area of an
unbounded
region.
There are two ways that an integral can be improper: it has an
Definition of an Improper Integral of Type 1:
For a fixed number
a
, we define the improper
integral
Z
1
a
f
(
x
)
dx
using a limit:
if this limit exists (as a finite number).
If the limit exists, then we say the improper integral
converges
. Otherwise, the integral
di-
verges
.
The improper integral
Z
a
-1
f
(
x
)
dx
is defined as above, and
Example 1:
Determine whether
Z
1
1
1
x
dx
converges or diverges, and evaluate if possible.
1 of 4
infinite
integral
i e
or
is
a
limit of
integration
on
the
bounds
an
infinite
discontunity
i.e
is
a
vertical
asymptote
flxtdx
fijno.SI
faddy
i
a
t
fig
Sea
fix
d
Break
into
2
To
fix
d
f.aoofcxldxtfaofc.de
cases
for
any
number
a
that
is conoient make
a
any
term
Evacuate
J
de
If
noo
Sit
DX
the
integral
ist
i
In
11
i
i