Question : The rate of growth of a microbe population is given by m'(x) = 30xe^2x : 2158468

Use the Trapezoidal Rule to approximate the ∫ using the indicated value of n.

62) ; n = 4, Write answer as a whole number or reduced fraction.

A) 33

B) (45/2)

C) 16

D) (33/2)

63) dx; n = 4, Round to two decimal places.

A) 1.62

B) 1.12

C) 1.02

D) 1.42

64) ; n = 4, Round to three decimal places.

A) 6.071

B) 3.809

C) 12.142

D) 3.036

Use Simpson's rule to approximate the ∫ using the indicated value of n (so there are 2n subintervals).

65) ; n = 4, Round to three decimal places.

A) 4.236

B) 4.424

C) 4.024

D) 3.616

66)  dx; n = 4, Round to two decimal places.

A) 0.89

B) 1.10

C) 1.24

D) 1.33

67) dx; n = 2, Round to two decimal places.

A) 1.46,

B) 1.33

C) 1.29

D) 1.20

68) dx; n = 4, Round to two decimal places.

A) 1.03

B) 1.11

C) 1.21

D) 1.13

69) dx; n = 4, Round to two decimal places.

A) 0.24

B) 0.20

C) 0.34

D) 0.30

70) ; n = 4, Write answer as whole number or reduced fraction.

A) (115/3)

B) 92

C) 23

D) 46

71) ; n = 4, Write answer as whole number or reduced fraction.

A) (101/24)

B) (145/16)

C) (101/12)

D) (161/24)

Find the indefinite ∫ using a table of integration formulas.

72) ∫(√(16x² + 96)) dx

A) (1/2)[x√(x² + 6) + 6ln(x + √(x² + 6))] + C

B) (1/2)[x√(16x² + 96) + 96ln(x + √(16x² + 96))] + C

C) 2[x√(x² + 6) + 6ln(x + √(x² + 6))] + C

D) 2[x√(x² + 96) + 96ln(x + √(x² + 96))] + C

73) ∫(√(x² + 9))dx

A) (1/4)(x√(x² + 9) + 9ln|x + √(x² + 9) |) + C

B) (1/2)(x√(x² + 9) + ln|x + √(x² + 9) |) + C

C) (1/2)(x√(x² + 9) + 9ln|x + √(x² + 9)|) + C

D) (1/4)(x√(x² + 9) + ln|x + √(x² + 9) |) + C

74) ∫((1/√(x² - 16)))dx

A) ln(x + √(x² - 16)) + C

B) (1/8)ln((4 + x/4 - x)) + C

C) (1/8)ln((x - 4/x + 4)) + C

D) ln(x + √(x² + 16)) + C

75) ∫((1/√(x² - 49))dx)

A) ln|x + √(x² - 49)| + C

B) ln|x + √(x² + 49)| + C

C) (1/14)ln|(7 + x/7 - x)| + C

D) (1/14)ln|(x - 7/x + 7)| + C

76) ∫(x√(x⁴ + 81) dx)

A) (1/4)(x²√(x⁴ + 81) + 81ln|x² + √(x⁴ + 81)|) + C

B) (1/2)(x√(x⁴ + 81) + ln|x + √(x⁴ + 81) |) + C

C) (1/4)(x√(x⁴ + 81) + 81ln|x + √(x⁴ + 81) |) + C

D) (1/4)(x√(x⁴ + 81) + ln|x + √(x⁴ + 81) |) + C

77) ∫((x/(4 + 5x)(5 + x)))dx

A) (4/21)ln|4 + 5x| + (5/105)ln|5 + x| + C

B) - (4/105)ln|4 + 5x| + (5/21)ln|5 + x| + C

C) - (4/21)ln|4 + 5x| + C

D) - (4/21)ln|4 + 5x| + (5/105)ln|5 + x| + C

78) ∫((2/5x (7x + 7)))dx

A) (2/35)ln|(x/7x + 7)| + C

B) (1/7) + (x/7) - (1/7)ln|7x + 7| + C

C) (2/7)ln|(x/7x + 7)| + C

D) (1/7)ln|(x/7x + 7)| + C

Provide an appropriate response.

79) Use an integral table to find ∫(x³ e^2x) dx.

A) (x³e^2x/2) - (3x²e^2x/4) - (3xe^2x/4) + C

B) (x³e^2x/2) - (3x²e^2x/4) - (3xe^2x/4) - (3e^2x/8) + C

C) (x³e^2x/2) + (3x²e^2x/4) - (3xe^2x/4) - (3e^2x/8) + C

D) (x³e^2x/2) - (3x²e^2x/4) - (3e^2x/8) + C

80) Use the integral table to find ∫(x e^3x dx .)

A) (x e^3x/3) - (e^3x/9) + C

B) (x e^3x/3) - (e^3x/3) + C

C) (x e^3x/3) + (e^3x/9) + C

D) x e^3x - (e^3x/3) + C

81) Use an integral table to find ∫(9x⁶lnx dx).

A) x⁷|(lnx/7) - (1/49)| + C

B) 9x⁷|(lnx/7) - (1/49)| + C

C) 9xlnx - 9x + C

D) (x⁷/9)|(lnx/7) - (1/49)| + C

Solve the problem.

82) The rate of growth of a microbe population is given by m'(x) = 30xe^2x, where x is time in days. What is the net growth between day 3 and day 7?

A) 222,613,544

B) 117,238,789

C) 111,306,789

D) 222,613,533