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Region Bounded - Calculus - Exam, Exams of Calculus

Guru Jambheshwar University of Science and TechnologyCalculus

Some keywords from this exam paper are: Region, Integral, Minimal Value, Approximates, Absolute Error, Minimal Positive Number, Region, Area, Length, Solid of Revolution

Typology: Exams

2012/2013

Uploaded on 03/16/2013

parni
parni 🇮🇳

4.1

(14)

100 documents

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MATH106B CALCULUS II - PROF. P. WONG
EXAM I - FEBRUARY 3, 2006
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. 20
4. 20
5. 20
Total 100
1
pf3
pf4
pf5

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MATH106B CALCULUS II - PROF. P. WONG

EXAM I - FEBRUARY 3, 2006

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. 20
  4. 20
  5. 20 Total 100

1

2 EXAM I - FEBRUARY 3, 2006

1.(16 pts.)(a) Consider the region bounded by the graph of y = 2x − x^2 and the graph of y = x^4. Find the exact area of the region. [Make a sketch of the region first.]

(4 pts.)(b) Write (DO NOT evaluate) a definite integral representing the arc-length of the path given by y = 2x − x^2 from the origin (0,0) to the point (1,1).

4 EXAM I - FEBRUARY 3, 2006

3.(20 pts.) The region bounded by the graph of y = √x, the x-axis, and the line x = 2 is revolved about the y-axis. Find the exact volume of the resulting solid of revolution. [Sketch a picture of the region and the solid.]

MATH106B CALCULUS II - PROF. P. WONG 5

4.(10 pts.)(a) Evaluate the indefinite integral ∫ (^2) x (^3) − x 2 2 x^2 − x − 3 dx.

(10 pts.)(b) Evaluate the definite integral ∫ (^) e 1

ln x x^2 dx.