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Exam 3 Questions with Solutions for Calculus II | MATH 211, Exams of Calculus

Millersville University of Pennsylvania (MU)Calculus

Material Type: Exam; Class: Calculus 2; Subject: Mathematics; University: Millersville University of Pennsylvania; Term: Summer 3 2008;

Typology: Exams

Pre 2010

Uploaded on 08/17/2009

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koofers-user-xb9 🇺🇸

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Millersville University Name
Department of Mathematics
MATH 211, Calculus II, Test 3
August 7, 2008
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit. The
point values of the problems are listed in parentheses.
1. (10 points) Find the exact area of the region bounded by the graphs of y=x2,y= 0,
and x= 2.
2. (10 points) Find the volume of the solid of revolution generated by revolving the region
bounded between y=x2and y= 2xabout the x-axis.
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Millersville University Name Department of Mathematics MATH 211, Calculus II, Test 3 August 7, 2008

Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses.

  1. (10 points) Find the exact area of the region bounded by the graphs of y = x^2 , y = 0, and x = 2.
  2. (10 points) Find the volume of the solid of revolution generated by revolving the region bounded between y = x^2 and y = 2x about the x-axis.
  1. (10 points) Write out the first five nonzero terms of the Maclaurin series for g(x) = ex^ − x^2.
  2. (10 points) The region bounded by x = 4 − y^2 and x = y^2 − 4 is revolved around the line where y = 5. Using the method of shells, set up the definite integral for finding the volume of the solid of revolution. You do not need to evaluate the definite integral.
  1. (10 points) The graph of y = cos 2x over the interval [0, π] is revolved around the x-axis. Set up the definite integral for finding the surface area of the resulting solid of revolution. You do not need to evaluate the definite integral.
  2. (10 points) A force of 55 pounds stretches a spring 10 inches. Find the work done stretching the spring 6 inches beyond its natural length.
  1. (10 points) Compute the mass and center of mass of an object lying along the x-axis with 0 ≤ x ≤ 2 if the linear density of the object is given by ρ(x) = x^2 − x + 6.