#### Riemann & Trapezoidal Sums - 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

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## Collection Contents

### Riemann Sum Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 2 (and its solution) covers computing the right endpoint Riemann sum of an integral and then using that answer to evaluate a limit. 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Riemann Sums and Integrals Exam Questions

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 4.1 through 4.3 (and their solutions) cover evaluating Riemann sums and integrals. 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Trapezoid Rule and Simpsons Rule Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 9 (and its solution) covers finding the approximate value of an integral using each rule with two subintervals. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Trapezoid Rule and Simpson's Rule: Baseball Stats Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 5 (and its solution) covers estimating the number of hits a player got in a month using the two rules. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Numeric Approximations of Integrals Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 2 (and its solution) covers using Riemann Sums, the Trapezoid Rule, and Simpson's Rule to approximate a definite integral. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Trapezoidal Rule Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Question 9 (and its solution) covers estimating a definite integral of the sine-squared function using three intervals of the Trapezoidal Rule. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Definite Integrals Exam Question

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 3B-1 through 3B-7 (and their solutions) cover using sigma notation for sums, computing Riemann sums for definite integrals, and evaluating limits by relating them to Riemann sums. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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### Numerical Integration Exam Questions

by Massachusetts Institute of Technology MIT OpenCourseware

Single Variable Calculus Questions 3G-1 through 3G-5 (and their solutions) cover approximating integrals using Riemann sums, the Trapezoidal Rule, and Simpson's Rule. Course: 18.01 Single Variable Calculus, Fall 2006Instructor: 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 http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode
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