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Question : A particle moves so that its velocity (in m/s) is given by v = 2te^-t : 2151795

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the table of ∫s or a computer or calculator with symbolic integration capabilities to find the interal.

1) ∫((4xdx/x^{2}(1 + 4x^{2})))

A) ln|(1 + 4x^{2}/x^{2})|+ C

B) ln|(x^{2}/1 + 3x^{2})|+ C

C) - 3ln|(1 + 3x^{2}/x^{2})|+ C

D) - 2ln|(1 + 4x^{2}/x^{2})|+ C

2) ∫((dx/x√(6 + 4x)))

A) ln|(√(6 + 4x) + √(6)/√(6 + 4x) - √(6))|+ C

B) (1/√(6))ln((√(6 + 4x) - √(6)/√(6 + 4x) + √(6))) + C

C) ln|(√(6 + 4x) - √(6)/√(6 + 4x) + √(6))|+ C

D) (1/√(6))ln|(√(6 + 4x) - √(6)/√(6 + 4x) + √(6))|+ C

3) ∫((xdx/√(1 + x)))

A) (x - 2) √(1 + x) + C

B) ((x - 2)√(1 + x)/3) + C

C) (4(x - 2) √(1 + x)/3) + C

D) (2(x - 2)√(1 + x)/3) + C

4) ∫((4/√(x^{2} + 9))dx)

A) 4ln|x + √(x^{2} + 3)|+ C

B) (4/3) tan^{-1} (x/3) + C

C) - (4/3)ln|(3 + √(x^{2} + 9)/x)|+ C

D) 4ln|x + √(x^{2} + 9)|+ C

5) ∫((4/49 - x^{2})dx)

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

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

C) 4sin^{-1}(x/7) + C

D) (4/7)tan^{-1}(x/7) + C

6) ∫((dx/5x^{2} + 9x))

A) (1/9)ln|(x/5x + 9)|+ C

B) (1/5)tan^{-1}(x/5) + C

C) (1/5)ln|(1/5x + 9)|+ C

D) (1/5)ln|5x^{2} + 9x|

7) ∫((1/√(x^{2} - 64)))dx

A) (1/16)ln((x - 8/x + 8)) + C

B) ln(x + √(x^{2} + 64)) + C

C) ln(x + √(x^{2} - 64)) + C

D) (1/16)ln((8 + x/8 - x)) + C

8) ∫((1/x√(9 + x^{2})))dx

A) (1/3)ln((3 + √(9 + x^{2})/x)) + C

B) - (1/3)ln((3 + √(9 + x^{2})/x)) + C

C) - (1/3)ln((3 + √(9 - x^{2})/x)) + C

D) ln(x + √(x^{2} + 9)) + C

9) ∫((2/5x (3x + 7)))dx

A) (2/35)ln((x/3x + 7)) + C

B) (1/7)ln((x/3x + 7)) + C

C) (7/9) + (x/3) - (7/9)ln(3x + 7) + C

D) (2/7)ln((x/3x + 7)) + C

10) ∫(√(25x^{2} + 50))dx

A) (5/2)[x√(x^{2} + 50) + 50ln(x + √(x^{2} + 50))] + C

B) (1/2)[x√(25x^{2} + 50) + 50ln(x + √(25x^{2} + 50))] + C

C) (1/2)[x√(x^{2} + 2) + 2ln(x + √(x^{2} + 2))] + C

D) (5/2)x√(25x^{2} + 50 ) + 25ln(x + √(25x^{2} + 50)) + C

Solve the problem.

11) A particle moves so that its velocity (in m/s) is given by v = 2te^{-t}, where t is the time (in seconds). Find the distance traveled between t = 0 and t = 3.

A) 2.2

B) 1.6

C) 0.92

D) 3.86

12) The rate of growth of a microbe population is given by m'(x) = 30xe^{2x}, where x is time in days. What is the growth after 1 day?

A) 62.92

B) 55.42

C) 62.52

D) 110.84

13) 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 1 and day 3?

A) 30,161

B) 15,073

C) 15,062

D) 30,175

14) 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

15) Find the area between y = (x - 4)ex and the y-axis from x = 4 to x = 7. Give your answer in exact form.

A) 2e^{7} + e^{4}

B) e^{7} - e^{4}

C) 2e^{7}

D) e^{7} + e^{4}

16) Find the area between y =lnx and the x-axis from x = 1 to x = 4. Give your answer in exact form.

A) ln4

B) 4ln4 - 3

C) (3/4)

D) 4ln4 - 4

17) The rate of water usage for a business, in gallons per day, is given by W(t) = 619te^{-t}, where t represents the number of hours since midnight. Approximately how many gallons of water does the business use in the first 6 hours of the day?

A) 608 gallons

B) 630 gallons

C) 611 gallons

D) 11 gallons

18) A person's metabolic rate tends to go up after eating a meal and then, after some time has passed, it returns to a resting metabolic rate. This phenomenon is known as the thermic effect of food, and the effect (in kJ/hr) for one individual is

F(t) = -10.28 + 175.9te^{-t/1.3}

where t is the number of hours that have elapsed since eating a meal. Find the total thermic energy of a meal for the next four hours after a meal by integrating the thermic effect function between t = 0 and t = 4.

A) 128.4 kJ

B) 150.1 kJ

C) 200.3 kJ

D) 186.5 kJ