Answer Key
829
2 −9 2 ≈ − 0.8055 m;
total distance traveled: 4ln4−7.5+ e 2
5.22 . Net displacement: e
m
2 ≈1.740
5.23 . 17.5 mi 5.24 . 64 5 5.25 . ⌠ ⌡ 3 x 2 ⎛
3
2
⎞ ⎠
⎛ ⎝ x 3 −3
⎞ ⎠
⎝ x 3 −3
dx = 1 3
+ C
⎞ ⎠ 10 30 +
⎛ ⎝ x 3 +5
5.26 .
C
5.27 . − 1
+ C
sin t
4 t 4 +
5.28 . − cos
C
5.29 . 91 3 5.30 . 2
3 π ≈0.2122
5.31 . ⌠ 5.32 . ⌠
3
3
2 e −2 x
e −2 x
⌡ x
dx = − 1 6
+ C
e x −2) 3
x (3 e x −2) 2 dx = 1
⌡ e
9 (3
5.33 . ∫ 2 x 3 e x 4
4
e x
dx = 1 2
⌠ ⌡ 0 4
e u du = 1 2 ⎛
⎞ ⎠
5.34 . 1 2
⎝ e 4 −1
5.35 . Q ( t ) = 2 t ln2
+8.557. There are 20,099 bacteria in the dish after 3 hours.
5.36 . There are 116 flies. 5.37 . ⌠ ⌡ 1 2 1 x 3 e 4 x −2 dx = 1 8 ⎡
⎤ ⎦
⎣ e 4 − e
5.38 . ln | x +2 | + C 5.39 . x ln3
(ln x −1)+ C
5.40 . 1
−1 (4 x )+ C
4 sin
⎛ ⎝ x 3
⎞ ⎠ + C
5.41 . sin −1
−1 ⎛
⎞ ⎠ + C
⎝ 2 x 5
5.42 . 1 5.43 . 1
10 tan
−1 ⎛
⎞ ⎠ + C
⎝ x 4
4 tan
5.44 . π 8 Section Exercises
1 . a. They are equal; both represent the sum of the first 10 whole numbers. b. They are equal; both represent the sum of the first 10 whole numbers. c. They are equal by substituting j = i −1. d. They are equal; the first sum factors the terms of the second.
3 . 385 − 30 = 355 5 . 15 − (−12) = 27 7 . 5(15) + 4(−12) = 27 9 . ∑ j =1 50 j 2 −2 ∑ j =1 50
j = (50)(51)(101) 6
− 2(50)(51) 2 =40, 375
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