James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A96 Appendix I Answers to Odd-Numbered Exercises
11. 11y30
y
y
31. (a) 2 y 1 0 e22x 2 dx < 3.75825
y=1
y=≈
2
y=1
(b) 2 y 1 0
( e
22x 2 1 2e 2x 2 ) dx < 13.14312
33. (a) 2 y 2 0 8s1 2 x 2 y4 dx < 78.95684
(b) 2 y 1 0 8s4 2 4y 2 dy < 78.95684
π
”_ 3 , 3’
y
0 1
x=y@
y=3 π
” 3 , 3’
y=1+sec x
13. 2s 4 3 2 s3d ms80547-1 & 547-2
x
y
0 1
x
35. 24.091, 21.467, 1.091; 89.023 37. 11 8 2
39. Solid obtained by rotating the region 0 < x < ,
0 < y < ssin x about the x-axis
41. Solid obtained by rotating the region above the x-axis
bounded by x − y 2 and x − y 4 about the y-axis
43. 1110 cm 3 45. (a) 196 (b) 838
47. 1 3 r 2 h 49. h 2 sr 2 1 hd 3 51. 2 3 b 2 h
53. 10 cm 3 55. 24 57. 1 3 59. 8 15 61. 4y15
63. (a) 8R y r sr 0 2 2 y 2 dy (b) 2 2 r 2 R
65. (b) r 2 h 67. 5 12 r 3 69. 8 y r 0 sR 2 2 y 2 sr 2 2 y 2 dy
0 x
y=1 y=1
0 x
Exercises 6.3 • page 453
1. Circumference − 2x, height − xsx 2 1d 2 ; y15
15. 3y5
y
1
0
y
1
0
17. 10s2 y3
y
0 1
y
1
2
0 1
y=x#
1
2
{ , œ„ }
1
6et 6.2.13
8.26.06
x=2
x
1 3 4
x=2
y=1-¥
x=3
x=¥
x=3
19. y3 21. y3 23. y3
25. 13y45 27. y3 29. 17y45
x
x
x
3. 6y7 5. s1 2 1yed 7. 8
9. 4 11. 192 13. 16y3
15. 264y5 17. 8y3 19. 13y3
21. (a) 2 y 2 0 x 2 e 2x dx (b) 4.06300
23. (a) 4 y y2
2y2 s 2 xd cos4 x dx (b) 46.50942
25. (a) y 0
2s4 2 ydssin y dy (b) 36.57476
27. 3.68
29. Solid obtained by rotating the region 0 < y < x 4 , 0 < x < 3
about the y-axis
31. Solid obtained (using shells) by rotating the region
0 < x < 1yy 2 , 1 < y < 4 about the line y − 22
33. 0, 2.175; 14.450 35. 1 32 3 37. 8
39. 4s3 41. 4y3
43. 117y5 45. 4 3 r 3 47. 1 3 r 2 h
Exercises 6.4 • page 458
1. (a) 7200 ft-lb (b) 7200 ft-lb
3. 4.5 ft-lb 5. 180 J 7. 15 4 ft-lb
9. (a) 25
24 < 1.04 J (b) 10.8 cm 11. W2 − 3W1
13. (a) 625 ft-lb (b) 1875
4 ft-lb 15. 650,000 ft-lb
17. 3857 J 19. 62.5 ft-lb 21. 2450 J
23. <1.06 3 10 6 J 25. 1.04 3 10 5 ft-lb 27. 2.0 m
31. (b) 161.3 ft-lb
33. (a) Gm 1m 2S 1 a 2 1 bD (b) <8.50 3 10 9 J
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