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September 8, 2008

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Teachers and students can use these exam questions and solutions to test the information learned.

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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- Mathematics > General
- Mathematics > Calculus

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Table of Contents

- Evaluating Definite Integrals Exam Question
- Miscellaneous Integration Problems Exam Questions
- Integration by Parts I Exam Question
- Partial Fractions Exam Question
- Techniques of Antidifferentiation I Exam Question
- Integration by Parts II Exam Questions
- Trigonometric Substitution I Exam Question
- Techniques of Antidifferentiation II Exam Question
- Integration by Substitution Exam Questions
- Antiderivatives of Inverse Trigonometric Functions Exam Questions
- Definite Integrals I Exam Question
- Definite Integrals II Exam Question
- Indefinite Integrals: Ratio of Polynomials I Exam Question
- Trigonometric Substitution II Exam Question
- Reduction Formulas Exam Question
- Trigonometric Substitution III Exam Question
- Indefinite Integrals: Ratio of Polynomials II Exam Question
- Indefinite Integrals Exam Questions
- Trigonometric Substitution IV Exam Question
- Evaluating Integrals Exam Question
- Trigonometric Substitution V Exam Question
- Differentials and Indefinite Integration Exam Questions
- Change of Variables and Estimating Integrals Exam Questions
- Integration Exam Questions

Teachers and students can use these exam questions and solutions to test the information learned.

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc

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Single Variable Calculus Question 4 (and its solution) covers evaluating integrals involving the substitution method, logarithmic functions, and trigonometric functions.

Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Single Variable Calculus Questions I.1 through IV.5 (and their solutions) cover four topics.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 1 (and its solution) covers computing an antiderivative using the method of integration by parts.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 3 (and its solution) covers finding the partial fraction decomposition of a fraction of two polynomials and using it to find the antiderivative of that function.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 4 (and its solution) covers evaluating an antiderivative that requires the application of multiple techniques.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Questions 1 and 2 (and their solutions) cover evaluating a definite and indefinite integral using the method of integration by parts.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 7 (and its solution) covers evaluating an integral using the method of trigonometric substitution.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 12 (and its solution) covers evaluating four integrals using multiple techniques.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Questions 4.4 through 4.5 (and their solutions) cover evaluating a definite integral.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Questions 6.4 through 6.7 (and their solutions) cover evaluating antiderivatives of the inverse sine, cosine, and tangent functions.Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2005

Instructor: Prof. Jason Starr

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Single Variable Calculus Question 1 (and its solution) covers two integrals that need to be evaluated.http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Single Variable Calculus Question 1 (and its solution) covers two integrals that need to be evaluated.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1 (and its solution) covers antidifferentiating a function which is a ratio of polynomials.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 2 (and its solution) covers evaluating a definite integral using a suggested trigonometric substitution.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 3 (and its solution) covers finding a reduction formula for two integrals involving exponentials.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 1 (and its solution) covers evaluating a definite integral using a trigonometric substitution.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 3 (and its solution) covers antidifferentiating a function which is a ratio of polynomials.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 1and 2 (and their solutions) cover evaluating indefinite integrals using advanced techniques.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 3 (and its solution) covers evaluating a definite integral using a trigonometric substitution.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 12 (and its solution) covers two integrals that need to be evaluated, one involving a ratio of polynomials, the other involving a natural logarithm.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Question 13 (and its solution) covers evaluating a definite integral using the trigonometric substitution of the tangent function.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 3A-1 through 3A-3 (and their solutions) cover evaluating five differentials and twenty indefinite integrals using a range of techniques.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 3E-1 through 3E-7 (and their solutions) cover evaluating or estimating integrals by using the method of substitution of variables.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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Single Variable Calculus Questions 5B-1 through 5F-6 (and their solutions) cover integrals to be evaluated using the method of substitution; integrals to be evaluated, each of which involves a trigonometric function; integrals to be evaluated using the method of inverse substitution and completing the square; integrals that must be evaluated using the method of partial fractions; evaluating integrals using the method of integration by parts or deriving reduction formulas.Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

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