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
