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Chp 78
Improper Integrals
Notes
1.
There are two types of
IMPROPER INTEGRALS to consider:
(1) When the interval
[a, b]
involves
(2) When the function
f(x)
is discontinuous within the interval [a, b]
2.
INTEGRALS WITH INTERVALS INVOLVING
Ex(consider area under a curve)
—
Look at the area of
f(x) =
on the interval
[1, t]
where
t
A
=
dx
=
(apply the F.T.C.)
=
+ 1
What is the area when
t = 2 ?
t = 3 ?
t = 5 ?
t = 10 ?
A = 1/2
A = 2/3
A = 4/5
A = 9/10
What about when
t
?
The area, surprisingly
(maybe not?)
, is not a value near
.
The integral is improper if it is set up as
dx .
The interval [a, b] has to be endpoints with specific number values.
Since
t
is not a specific number,
LIMITS are used with integrals.
dx
=
=
0 + 1
=
1
area under the curve
maximum area approached
3.
THREE CASES WHERE INTERVALS CAN INVOLVE
(1)
f(x) dx
=
=
(2)
f(x) dx
=
=
(3)
f(x) dx
=
f(x) dx
+
f(x) dx
where
c
is your choice
+
+
f(x)
x
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 Spring '10
 KNOPF
 Improper Integrals, Integrals

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