Question : 1) f(x) = 2x + 3 from x = 0 to x = 2; n = 4; use right endpoints : 2151776

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

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

1) f(x) = 2x + 3 from x = 0 to x = 2; n = 4; use right endpoints

A) 15

B) 13

C) 11

D) 17

2) f(x) = 3x² - 2 from x = 1 to x = 5; n = 4; use right endpoints

A) 154

B) 140

C) 150

D) 144

3) f(x) = (7/x) from x = 2 to x = 6; n = 4; use right endpoints

A) 7.63

B) 8.98

C) 9.33

D) 6.65

4) f(x) = (1/x²); interval [1, 5]; n = 4; use left endpoints

A) 0.4636

B) 2.0833

C) 1.4236

D) 1.4636

5) f(x) = x² + 2; interval [0, 5]; n = 5; use left endpoints

A) 65

B) 40

C) 32

D) 66

6) f(x) = x² from x = 0 to x = 3 n = 2; use midpoints

A) 12.5

B) 16.875

C) 8.4375

D) 3.375

7) f(x) = e^-x + 2 from x = -2 to x = 6; n = 4; use right endpoints

A) 22.29

B) 18.31

C) 16.02

D) 33.09

8) f(x) = (1/x) from x = 3 to x = 9; n = 2; use midpoints

A) (136/2025)

B) (16/45)

C) (32/45)

D) (68/675)

9) f(x) = 16 - x² from x = -4 to x = 4; n = 2; use midpoints

A) 96

B) 32

C) 48

D) 8

10) f(x) = 2x³ - 1 from x = 1 to x = 6; n = 5; use right endpoints

A) 800

B) 850

C) 825

D) 875

Find the exact value of the integral using a formula from geometry.

11) dx

A) (25π/4)

B) 25π

C) 50π

D) (25π/2)

12) dx

A) 60

B) 30

C) 24

D) 48

13) dx

A) 1

B) 8

C) 4

D) 2

14) dx

A) 50π

B) (25π/2)

C) (25π/4)

D) 25π

15) for the indicated region.

A) 10

B) 12.5

C) 5

D) 7.5

16) for the indicated region.

A) 42

B) 14

C) 7

D) 49

Solve the problem.

17) The table below shows the velocity of a remote-controlled race car moving along a dirt path for 8 seconds. Estimate the distance traveled by the car using 8 subintervals of length 1 with left endpoints.

A) 238 in.

B) 124 in.

C) 109 in.

D) 119 in.

18) The table below shows the velocity of a remote-controlled race car moving along a dirt path for 8 seconds. Estimate the distance traveled by the car using 8 subintervals of length 1 with right endpoints.

A) 184 in.

B) 194 in.

C) 188 in.

D) 178 in.

19) Joe wants to find out how far it is across the lake. His boat has a speedometer but no odometer. The table below shows the boat's velocity at 10-second intervals. Estimate the distance across the lake using right endpoints.

A) 5000 ft

B) 3370 ft

C) 337 ft

D) 3470 ft

20) A piece of tissue paper is picked up in gusty wind. The table below shows the velocity of the paper at 2-second intervals. Estimate the distance the paper traveled using right endpoints.

A) 107 ft

B) 191 ft

C) 194 ft

D) 214 ft

21) In the table below, the velocity of a projectile fired straight into the air is given every half second. Use right endpoints to estimate the distance the projectile traveled in four seconds.

A) 894.8 m

B) 427.8 m

C) 447.4 m

D) 855.6 m

22) A swimming pool has a leak, and the leak is getting worse. The table below gives the leakage rate every 6 hours. Use right endpoints to estimate the number of gallons lost in 48 hours.

A) 196.8 gal

B) 32.8 gal

C) 145.2 gal

D) 256.8 gal

23) The graph below shows the rate of natural gas usage (in therms per day) in one household for a 30-day period. Estimate the total number of therms used during this period. Use left endpoints and rectangles with widths of 3 days.

A) 136 therms

B) 147 therms

C) 159 therms

D) 165 therms

24) The graph below shows the rate of change of the price of a stock (in dollars per share per week) over a period of 6 weeks. Estimate the total change in dollars per share of the stock during this period. Use rectangles with widths of 1 week, and let the function value at the midpoint of the rectangle give the height of the rectangle.

A) $2.00/share

B) $1.60/share

C) $2.20/share

D) $0.90/share

Provide the proper response.

25) The definite integral represents area only if the function involved is ____ at every x-value in the interval [a, b].

A) rational

B) negative

C) positive

D) nonnegative

26) If f(a) = 3 and f(x) is increasing on the interval [a, b], then which method of estimating the area under the graph of f(x) and above the x-axis will yield the highest value? Assume that n = 10 in all cases.

A) Using right endpoints

B) Using midpoints

C) Using left endpoints

D) Cannot be determined

27) If f(b) = 4 and f(x) is decreasing on the interval [a, b], then which method of estimating the area under the graph of f(x) and above the x-axis will yield the lowest value? Assume that n = 10 in all cases.

A) Using left endpoints

B) Using right endpoints

C) Using midpoints

D) Cannot be determined

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

28) What is the difference between the indefinite ∫ and the definite ∫?

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

29) In estimating the definite integral for f(x) on the interval [5, 10], we compute Δx = (b - a/n). If n = 5, then what is the value of Δx?

A) 2

B) 5

C) 2.5

D) None of the above

30) If f(x) gives the rate of change of F(x) for x in [a, b], thenrepresents

i) the total change in F(x) as y goes from a to b.

ii) the total change in F(x) as x goes from a to b.

iii) the total change in f(x) as x goes from a to b.

A) Only i is correct.

B) Either ii or iii could be correct.

C) Only ii is correct.

D) Only iii is correct.