math

MTH 135 FINAL Exam – Week 10

Name___________________________________ Date: _______________________

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

Set up a definite integral that represents the shaded area.

1) y = h(x)

`` 1) _______

A) B) C) D)

Provide an appropriate response.

2) Find the area between the graph of and the x-axis over the interval 2) _______

A) 92 B) -92 C) 372 D) 269

3) Find the area between the graph of and the x-axis over the interval (Round answer to two

decimal places.) 3) _______

A) 33.33 B) 333.33 C) 66.67 D) 666.67

Solve the problem.

4) The Lorenz curve for the income distribution in a certain country is given by

I) Find the Gini index of income concentration.

II) Use the answer found in I) to determine if the income of this country is more equally distributed, less equally

distributed, or distributed the same as a second country having an index of income concentration of 0.2. 4) _______

A) I) 0.25

II) more equally distributed B) I) 0.33

II) less equally distributed

C) I) 0.33

II) more equally distributed D) I) 0.25

II) less equally distributed

Evaluate the definite integral to two decimal places.

5) dt 5) _______

A) 145.69 B) 6.70 C) 27.29 D) 400.71

Solve the problem.

6) The length of telephone calls (in minutes) in a public telephone booth has the probability density function:

Determine the probability that a call selected at random will last longer than seven minutes. (Round answer to two

decimal places.) 6) _______

A) 0.42 B) 0.31 C) 0.54 D) 0.39

7) The rate of flow of a continuous income stream (in thousands of dollars per day) is given by Find the total

income produced during the first thirty days of operation. 7) _______

A) $3433.99 B) $343.40 C) $34,339.87 D) $34.34

8) Find the total income produced by a continuous income stream in the first four years if the rate of flow is

(Round answer to the nearest dollar.) 8) _______

A) $18,792 B) $2125 C) $2486 D) $564

Find the consumer's surplus for the following demand function at the given point.

9) D(x) = ; x = 9) _______

A) $3.25 B) $4.33 C) $4.50 D) $7.28

Solve the problem.

10) Find the equilibrium price if the price-demand equation is and the price-supply equation is

10) ______

A) $60.00 B) $13.00 C) $20.00 D) $7.00

Evaluate using integration by parts.

11) 11) ______

A) xex - 5ex + C B) 5ex - ex + C C) 5ex - 5xex + C D) 5xex - 5ex + C

12) 12) ______

A) ln x - - 4x + C B) ln x - + C

C) ln x - - 4x + C D) ln x - +4x + C

Illustrate the integral graphically and describe what the integral represents in terms of areas.

13)

13) ______

A) The integral represents the area

between the graph of y = ln 3x and

the x axis from x = 2 to x = 4.

B) The integral represents the area

between the graph of y = ln 3x and

the x axis from x = 2 to x = 4.

C) The integral represents the area

between the graph of y = ln 3x and

the x axis from x = 2 to x = 4.

D) The integral represents the negative of the

area between the graph of y = ln 3x and

the x axis from x = 2 to x = 4.

Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and

the x axis over that interval. Find the answer to two decimal places.

14) y = 2 - x , 0 ≤ x ≤ 3 14) ______

A) 1.05 B) -35.17 C) 37.27 D) -36.22

Solve the problem.

15) The rate of water usage for a business, in gallons per day, is given by where t = the number of hours

since midnight. Approximately how many gallons of water does the business use in the first 5 hours of the day?

15) ______

A) 26 gallons B) 631 gallons C) 674 gallons D) 622 gallons

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

16) ; n = 4, Write answer as a whole number or reduced fraction. 16) ______

A) 16 B) C) D) 33

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

17) dx; n = 4, Round to two decimal places. 17) ______

A) 0.30 B) 0.34 C) 0.24 D) 0.20

18) dx; n = 4, Round to two decimal places. 18) ______

A) 0.89 B) 1.10 C) 1.24 D) 1.33

19) ; n = 4, Write answer as whole number or reduced fraction. 19) ______

A) B) C) D)

Find the indefinite integral using a table of integration formulas.

20) 20) ______

A) B)

C) D)

21) 21) ______

A) B)

C) D)

Provide an appropriate response.

22) Use an integral table to find . 22) ______

A) + C B) 9x ln x - 9x + C

C) 9 + C D) + C

23) Find the area between the graph of and the x-axis over the interval (Round answer to two decimal

places.) 23) ______

A) 8 B) 10 C) - 8.67 D) 8.67

24) Find the area bounded by the parabolas y = 6x - and y = - 2x. (Round answer to three decimal places.)

24) ______

A) 22 B) 21.667 C) - 21.333 D) 21.333

Evaluate using integration by parts.

25) 25) ______

A) 5.0213 B) 14.2939 C) 1.4597 D) 2.8588