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Lecture Notes
PDF
Section 3, Page 5 to page 6
Fundamental Theorem of Calculus is presented and justified.
Prof. Jason Starr
Riemann Integrals (section 4 of lecture 14) and Derivatives (section 2 of lecture 1)
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PDF
Section 4, Page 7
General algorithm for evaluating integrals using the Fundamental Theorem of Calculus.
Prof. Jason Starr
Fundamental Theorem of Calculus (section 3 of this lecture)
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PDF
Section 1, Page 1 to page 2
Statement and explanation of the First and Second Fundamental Theorems, with examples.
Prof. David Jerison
None
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PDF
Section 4, Page 6 to page 7
An intuitive argument justifying the Second Fundamental Theorem and a complete proof of the First Fundamental Theorem, including remarks about these theorems as they relate to definite and indefinite integrals.
Prof. David Jerison
The Fundamental Theorems of Calculus (page 1 of this file)
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Online Textbook Chapter
Document
Statement and explanation of the two forms for the Fundamental Theorem of Calculus.
Prof. Daniel J. Kleitman
Anti-derivatives (OT19.1) and Riemann Sums (OT20.2)
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Exam Questions
PDF
Problem 4 (page 1)
Three part question finding bounds on the values of a function defined in terms of an integral and finding where the function is concave up or concave down.
Prof. David Jerison
None
Solution (PDF)# Page 1
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Problem 5 (page 1)
Using the Fundamental Theorem to evaluate an integral.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 3 (page 1)
Four part question which involves finding the derivative, critical points, and an estimation of a function which is defined in terms of an integral.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 5 (page 2)
Four part question which involves finding critical points and values of a function which is defined in terms of an integral.
Prof. David Jerison
None
Solution (PDF)# Page 2
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PDF
Problem 10 (page 2)
Finding the first and second derivatives of a function defined in terms of an integral, and expressing another integral in terms of that function.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF - 2.20 MB
Problem 3C-1 (page 22) to problem 3C-6 (page 22)
Six questions which involve finding areas under curves and evaluating definite integrals.
Prof. David Jerison
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