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Lecture Notes
PDF
Section 2, Page 2
Antiderivatives and indefinite integrals are defined. Constants of integration and integrands are also defined.
Prof. Jason Starr
Concept of derivative (section 2 of lecture 1)
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PDF
Section 3, Page 2 to page 3
Guess-and-check method for finding antiderivatives. Includes an example and some helpful rules.
Prof. Jason Starr
Antidifferentiation (section 2 of this lecture)
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Online Textbook Chapters
Document
Definition of the indefinite integral or anti-derivative and its use in finding information about a function when its derivative is known.
Prof. Daniel J. Kleitman
None
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Document
Discussion of the fact that any constant can be added to an antiderivative without changing the validity of that antiderivative.
Prof. Daniel J. Kleitman
Anti-derivatives (OT19.1)
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Document
Applying differentiation rules backwards to find anti-derivatives. A list of types of functions that can or cannot be anti-differentiated. Linearity of the operation of anti-differentiation.
Prof. Daniel J. Kleitman
Anti-derivatives (OT19.1)
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Document
Rules for integrating polynomials and other simple integrals by inspection, as well as techniques for integrating by substitution, parts, and partial fractions.
Prof. Daniel J. Kleitman
Anti-derivatives (OT19.1)
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Exam Questions
PDF
Problem 4 (page 6) to problem (page 7)
Five-part problem evaluating integrals involving the substitution method, logarithmic functions, and trigonometric functions.
Prof. Jason Starr
None
Solution (PDF) Pages 3 to 6
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PDF
Problem 2 (page 3)
Computing the antiderivative of a fraction of two polynomials.
Prof. Jason Starr
None
Solution (PDF) Pages 1 to 2
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PDF
Problem 9 (page 1)
Three integrals to be evaluated.
Prof. David Jerison
None
Solution (PDF)# Page 2
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PDF
Problem 3 (page 1)
Three integrals to be evaluated.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 5a (page 2)
Two integrals to be evaluated.
Prof. David Jerison
None
Solution (PDF)# Page 2
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PDF
Problem 1 (page 1)
Deriving a trigonometric formula and differentiating a logarithmic expression, then using those results to evaluate two integrals.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 1 (page 1)
Two integrals to be evaluated.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
(page 1)
A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.
Prof. David Jerison
None
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PDF - 2.2 MB
Problem 1E-1 (page 4) to problem 1E-5 (page 5)
Five questions which involve taking derivatives and antiderivatives of polynomials, finding the points on a graph which have horizontal tangent lines, and finding derivatives of rational functions.
Prof. David Jerison
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PDF - 2.2 MB
Problem 3A-1 (page 21) to problem 3A-3 (page 21)
Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.
Prof. David Jerison
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PDF - 2.2 MB
Problem 5A-1 (page 35) to problem 5A-6 (page 35)
Six questions which involve evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.
Prof. David Jerison
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