HH_Sec_5_4 - Math 10B Lecture Examples Section 5.4 Theorems...

(9/30/08)
Math 10B. Lecture Examples.
Section 5.4. Theorems about definite integrals †
Example 1 What is the integral of
g
from 1 to 8 if its integral from 1 to 5 is - 7 and its
integral from 5 to 8 is 9?
Answer:
integraldisplay
8
1
g
(
x
)
dx
= 2
Example 2 What is
integraldisplay
35
- 35
[
2p
(
x
) -
3q
(
x
)]
dx
if
integraldisplay
35
- 35
p
(
x
)
dx
=
10
and
integraldisplay
35
- 35
q
(
x
)
dx
=
20
?
Answer:
integraldisplay
35
- 35
[2
p
(
x
)
-
3
q
(
x
)]
dx
=
-
40
Example 3 What is
integraldisplay
0
3
Y
(
x
)
dx
if
integraldisplay
4
0
Y
(
x
)
dx
=
10
0 and
integraldisplay
3
4
Y
(
x
)
dx
= -
25
?
Answer:
integraldisplay
0
3
Y
(
x
)
dx
=
-
75
Example 4 What is
integraldisplay
3
0
[
2f
(
x
) -
4g
(
x
)]
dx
if
integraldisplay
3
0
f
(
x
)
dx
=
100
and
integraldisplay
3
0
g
(
x
)
dx
=
200
?
Answer:
integraldisplay
3
0
[2
f
(
x
)
-
4
g
(
x
))]
dx -
600
Example 5 Use the formulas for areas of rectangles and circles to evaluate