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Determining - Calculus - Exam, Exams of Calculus

National Institute of Industrial EngineeringCalculus

Key points of this past exam of Calculus are: Determining, Indefinite Integral, Exact Value, Definite Integral, Picture, Region Bounded, Points, Intersection, Curves, Region Described

Typology: Exams

2012/2013

Uploaded on 03/16/2013

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MATH106B,C CALCULUS II - PROF. P. WONG
EXAM I - SEPTEMBER 30, 2011
NAME:
Instruction: Read each question carefully. Explain ALL your work and give reasons to
support your answers.
Advice: DON’T spend too much time on a single problem.
Problems Maximum Score Your Score
1. 20
2. 20
3. 14
4. 6
5. 20
6. 20
Total 100
1
pf3
pf4
pf5

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MATH106B,C CALCULUS II - PROF. P. WONG

EXAM I - SEPTEMBER 30, 2011

NAME:

Instruction: Read each question carefully. Explain ALL your work and give reasons to support your answers.

Advice: DON’T spend too much time on a single problem.

Problems Maximum Score Your Score

  1. 20
  2. 20
  3. 14
  4. 6
  5. 20
  6. 20

Total 100

1

2 EXAM I - SEPTEMBER 30, 2011

1.(10 pts.)(a) Evaluate the indefinite integral (be sure to show all your work) ∫ ex^ sin(ex) dx.

(10 pts.) (b) Find the exact value of the definite integral (be sure to show all your work) ∫ (^2)

0

x^2 √ x^3 + 1

dx.

4 EXAM I - SEPTEMBER 30, 2011

  1. (14 pts.) Consider a function g on the interval [− 2 , 4].

x -2 -1 0 1 2 3 4 g(x) 1 0 -1 -2 1 3 4

Find L 6 , M 3 using the left-hand sum and the mid-point rule respectively for estimating the definite integral

− 2 g(x)^ dx.

  1. (6 pts.) Set up (do not evaluate) a definite integral for the arc length of the portion of the graph of f (x) = e−x^ sin x between x = 0 and x = π 2.

MATH106B,C CALCULUS II - PROF. P. WONG 5

  1. Let R be the region bounded by the curve 2(x − 2) = y^2 , the line y = 2, the line y = x, and the x-axis.

(10 pts.) (a) Set up (do not evaluate) a definite integral representing the volume of the solid obtained from rotating the region R around the line x = 0, i.e., the y-axis. [Hint: sketch a picture of the region R first.]

(10 pts.) (b) Find the exact volume of the solid described in part (a).