substitution. Sketch and label the associated dr 1. Í -2 sine
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Solve 1,3,5
![30. COs de
6:05
O X all 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 0 - 0 +C
= -4 - - sin
+ C
FIGURE S
--3- 2x - x - sin
+ C
7.3 EXERCISES
17. Í*
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. Íd
19.
dx
2.
V+ 4
*-2 tan
21. "-
dx
v9- 25x
22. Va+i de
V -4
3.
- 2 sec
23. j-
24. V - dx
+ 2x + 5
25. j+ 2x – x" de
26.a+ 4x - 4x
4-30 Evaluate the integral.
dx
4. Íd
27. j va + 2x de
19
28.
(x - 2x + 2)
5. j
V -1
de
6.
v36
dx
29. xT -x" dx
cos r
30. .
VI + sin'r
7. ya a>0
8.
a. - 16
dx
31. (a) Use trigonometric substitution to show that
9. "y
10. V4 - 9x ds
- In(x + V + a) + c
dr
11. ("- 4x dx
12.
v4 +
(b) Use the hyperbolic substitution - a sinh to show that
13. j - de
14. d
- sinh
+C
16. (
dx
These formulas are connected by Formula 3.11.3.
E sCm lea AR kd May d
d ti
ni
e a
O
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Transcribed Image Text:30. COs de
6:05
O X all 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 0 - 0 +C
= -4 - - sin
+ C
FIGURE S
--3- 2x - x - sin
+ C
7.3 EXERCISES
17. Í*
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. Íd
19.
dx
2.
V+ 4
*-2 tan
21. "-
dx
v9- 25x
22. Va+i de
V -4
3.
- 2 sec
23. j-
24. V - dx
+ 2x + 5
25. j+ 2x – x" de
26.a+ 4x - 4x
4-30 Evaluate the integral.
dx
4. Íd
27. j va + 2x de
19
28.
(x - 2x + 2)
5. j
V -1
de
6.
v36
dx
29. xT -x" dx
cos r
30. .
VI + sin'r
7. ya a>0
8.
a. - 16
dx
31. (a) Use trigonometric substitution to show that
9. "y
10. V4 - 9x ds
- In(x + V + a) + c
dr
11. ("- 4x dx
12.
v4 +
(b) Use the hyperbolic substitution - a sinh to show that
13. j - de
14. d
- sinh
+C
16. (
dx
These formulas are connected by Formula 3.11.3.
E sCm lea AR kd May d
d ti
ni
e a
O
く
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