Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 30EQ
Related questions
Question
Please solve only 9,11
![30. COs d
6:05 a
b •
O X al
l 66%i
View embed
IMG_5799.png
SECTION 7.3 Trigonometric Substitution
491
We now substitute u= 2 sin 8, giving du = 2 cos 8 de and 4 - u = 2 cos 6, so
Figure 5 shows the graphs of the inte-
grand in Example 7 and its indefinite
integral (with C- 0). Which is which?
2 sin e - 1
2 cos e
dx-
2 cos e de
2x
-
(2 sin - 1) de
--2 cos e - 0 +C
V4 - u - sin'
+ C
FIGURE S
2x - x - sin-
+ C
7.3 EXERCISES
17. f
dx
1-3 Evaluate the integral using the indicated trigonometric
substitution. Sketch and label the associated right triangle.
dx
18.
[lar)' - 6']
1.A
dx
1. E
I-2 sine
20. Íde
19.
dx
2.
V + 4
*-2 tan
21. "-
dx
v9- 25x
22. +Idr
V -4
- 2 sec
dx
24. V - dz
3.
23. j-
V+ 2x + 5
25. j+ 2x – x" de
26.a+ 4s- 4
4-30 Evaluate the integral.
de
4.
19
27. j v + 2x de
28.
(x - 2x + 2)
5. j
6.
v36
dx
29. xT -x" dx
cos r
30. .
VI + sin'r
7. ya a>0
8.
a. a- 16
9. "y
dx
31. (a) Use trigonometric substitution to show that
10. "4 - 9x dx
- In(x + y + a) + c
dr
11. ("- 4x dx
12.
v4 +
(b) Use the hyperbolic substitution - a sinh to show that
13. j - de
14. d
de
- sinh
+ C
16. (
dx
These formulas are connected by Formula 3.11.3.
D Cn leam AR d May d
e a
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Transcribed Image Text:30. COs d
6:05 a
b •
O X al
l 66%i
View embed
IMG_5799.png
SECTION 7.3 Trigonometric Substitution
491
We now substitute u= 2 sin 8, giving du = 2 cos 8 de and 4 - u = 2 cos 6, so
Figure 5 shows the graphs of the inte-
grand in Example 7 and its indefinite
integral (with C- 0). Which is which?
2 sin e - 1
2 cos e
dx-
2 cos e de
2x
-
(2 sin - 1) de
--2 cos e - 0 +C
V4 - u - sin'
+ C
FIGURE S
2x - x - sin-
+ C
7.3 EXERCISES
17. f
dx
1-3 Evaluate the integral using the indicated trigonometric
substitution. Sketch and label the associated right triangle.
dx
18.
[lar)' - 6']
1.A
dx
1. E
I-2 sine
20. Íde
19.
dx
2.
V + 4
*-2 tan
21. "-
dx
v9- 25x
22. +Idr
V -4
- 2 sec
dx
24. V - dz
3.
23. j-
V+ 2x + 5
25. j+ 2x – x" de
26.a+ 4s- 4
4-30 Evaluate the integral.
de
4.
19
27. j v + 2x de
28.
(x - 2x + 2)
5. j
6.
v36
dx
29. xT -x" dx
cos r
30. .
VI + sin'r
7. ya a>0
8.
a. a- 16
9. "y
dx
31. (a) Use trigonometric substitution to show that
10. "4 - 9x dx
- In(x + y + a) + c
dr
11. ("- 4x dx
12.
v4 +
(b) Use the hyperbolic substitution - a sinh to show that
13. j - de
14. d
de
- sinh
+ C
16. (
dx
These formulas are connected by Formula 3.11.3.
D Cn leam AR d May d
e a
II
く
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