Math 132 Exam #1 Spring 2019

Name __________________________________________________

Signature _______________________________________________

Student ID Number ____ ____ ____ ____ ____ ____ ____ ____

Section Number _________________________________________

Section Instructor Day/Time Section Instructor Day/Time

1 Mullath MWF 10:10 9 Bates TuThu 11:15

2 Mullath MWF 9:05 10 Dragon TuThu 1:00

3 Sinaei MWF 11:15 11 Lai MWF 11:15

4 Sinaei MWF 12:20 12 Nguyen TuThu 8:30

5 Zhai TuThu 2:30 13 Park MWF 10:10

6 Zhai TuThu 4:00 16 Torres TuThu 1:00

7 Farelli TuThu 8:30 17 Destromp MWF 1010

8 Farelli TuThu 10:00 18 Lai MWF 10:10

• Calculators, papers, phones, smart watches, any device, or notes are not permitted on this exam.

The use of any of these items is considered Academic Dishonesty.

• In the free response section, do not just give an answer. Clearly explain how you get it, providing

appropriate mathematical details.

• An answer with no corresponding work will be awarded zero points.

• This is a 2-hour exam.

Question Grade

Multiple Choice

Questions

(Out of 25)

6 (Out of 15)

7 (Out of 10)

8 (Out of 10)

9 (Out of 10)

10 (Out of 5)

11 (Out of 10)

12 (Out of 10)

13 (Out of 5)

Total (Out of 100)

2

Multiple Choice Section: Choose the one option that answers the question. There is no partial credit for

questions 1-5. Only answers written in the answer blank will be graded.

1. [5 points] Calculate 𝑔′(1) if 𝑔(𝑥) = ∫ √𝑡3 + 3𝑥5

0𝑑𝑡.

(A) 2

(B) 10

(C) 2 − √3 Answer: 1. _________

(D) 10 − √3

____________________________________________________________________________________

2. [5 points] A person wants to fill a 30,000-gallon swimming pool using a standard garden hose

with a flow rate of 𝑟(𝑡) = 300 + 200𝑡. Which of the following would be used to find the time,

𝑇, that it takes to fill the pool entirely?

(A) 300𝑇 + 100𝑇2 = 30,000

(B) 300 + 200𝑇 = 30,000

(C) ∫ (300 + 200𝑇)𝑑𝑇30,000

0

(D) 300 + 200(30,000)

Answer: 2. _________

3

3. [5 points] Evaluate the integral.

∫5 − sin(8𝑥)

8 𝑑𝑥

𝜋

0

(A) −5𝜋

8

(B) 5𝜋

8+

1

32

(C) 5𝜋

8 Answer: 3. _________

(D) 5𝜋

8−

1

32

____________________________________________________________________________________

4. [5 points] Which of the following represents the area between the curves 𝑦 = 3cos(𝑥) and

𝑦 = 1 + cos(𝑥) on 0 ≤ 𝑥 ≤ 𝜋.

(A) ∫ (2 cos(𝑥) − 1) 𝑑𝑥𝜋

0

(B) ∫ (2 cos(𝑥) − 1)𝑑𝑥 + ∫ (1 − 2 cos(𝑥))𝑑𝑥𝜋

𝜋/6

𝜋/6

0

(C) ∫ (1 − 2 cos(𝑥))𝑑𝑥 + ∫ (2 cos(𝑥) − 1)𝑑𝑥𝜋

𝜋/3

𝜋/3

0 Answer: 4. _________

(D) ∫ (2 cos(𝑥) − 1)𝑑𝑥 + ∫ (1 − 2 cos(𝑥))𝑑𝑥𝜋

𝜋/3

𝜋/3

0

4

5. [5 points] Which of the following is true about the graph below?

(A) ∫ 𝑓(𝑥)𝑑𝑥𝑐

𝑏≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑑

𝑏≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑑

𝑎

(B) ∫ 𝑓(𝑥)𝑑𝑥𝑐

𝑏≤ ∫ 𝑓(𝑥)𝑑𝑥 ≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑐

𝑎

𝑏

𝑎

(C) ∫ 𝑓(𝑥)𝑑𝑥𝑑

𝑏≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑑

𝑎≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑏

𝑎 Answer: 5. _________

(D) ∫ 𝑓(𝑥)𝑑𝑥𝑑

𝑏≤ ∫ 𝑓(𝑥)𝑑𝑥 ≤ ∫ 𝑓(𝑥)𝑑𝑥

𝑐

𝑏

𝑐

𝑎

5

Free Response Section: Show all work for each of the following questions. Partial credit may be

awarded for questions 6-13.

6a. [5 points] Sketch the graph of the curves 𝑥 = 𝑦2 and 𝑥 = 3𝑦. Then, calculate the area enclosed by

the curves.

6b. [10 points] Find the volume of the solid obtained by rotating the region enclosed by the curves

𝑥 = 𝑦2 and 𝑥 = 3𝑦 about the line 𝑥 = 9.

6

7. [10 points] A particle is moving along a line with the velocity function given by 𝑣(𝑡) = 𝑡2 − 8𝑡 + 12

measured in 𝑚/𝑠. Calculate the total distance traveled by the particle over the time interval

2 ≤ 𝑡 ≤ 10.

7

8. [10 points] Evaluate the integral.

∫4𝑥 + 12

(𝑥2 + 6𝑥 + 7)3𝑑𝑥

2

1

8

9. [10 points] Evaluate the integral.

∫ √9 − 4𝑥2 𝑑𝑥

9

10. [5 points] Evaluate the integral.

∫ln(4𝑥)

𝑥3𝑑𝑥

10

11. [10 points] Evaluate the integral.

∫ 𝑥17(𝑥9 + 1)15 𝑑𝑥

11

12. [10 points] Evaluate the integral. All trigonometric values must be simplified.

∫ sin4(𝑥) cos3(𝑥) 𝑑𝑥𝜋/6

0

12

13. [5 points] Evaluate the integral.

∫ 𝑒𝑥 cos(𝑥) 𝑑𝑥