# Antiderivatives From Derivatives of Basic Functions

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## Lecture Notes

#### Antidifferentiation

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Section 2, Page 2

Antiderivatives and indefinite integrals are defined. Constants of integration and integrands are also defined.

Instructor: Prof. Jason Starr
Prior Knowledge: Concept of derivative (section 2 of lecture 1)

#### Antidifferentiation: Guess-and-Check

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Section 3, Page 2 to page 3

Guess-and-check method for finding antiderivatives. Includes an example and some helpful rules.

Instructor: Prof. Jason Starr
Prior Knowledge: Antidifferentiation (section 2 of this lecture)

## Online Textbook Chapters

#### Introduction to Anti-Derivatives

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Definition of the indefinite integral or anti-derivative and its use in finding information about a function when its derivative is known.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: None

#### Non-Uniqueness of Anti-Derivatives

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Discussion of the fact that any constant can be added to an antiderivative without changing the validity of that antiderivative.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Anti-derivatives (OT19.1)

#### Anti-Derivatives by Inspection

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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.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Anti-derivatives (OT19.1)

#### Basic Techniques for Integrals

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Rules for integrating polynomials and other simple integrals by inspection, as well as techniques for integrating by substitution, parts, and partial fractions.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Anti-derivatives (OT19.1)

## Exam Questions

#### Evaluating Definite Integrals

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Problem 4 (page 6) to problem (page 7)

Five-part problem evaluating integrals involving the substitution method, logarithmic functions, and trigonometric functions.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Antiderivatives Using Polynomial Division

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Problem 2 (page 3)

Computing the antiderivative of a fraction of two polynomials.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Indefinite Integrals

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Problem 9 (page 1)

Three integrals to be evaluated.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Indefinite Integrals

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Problem 3 (page 1)

Three integrals to be evaluated.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Indefinite Integrals

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Problem 5a (page 2)

Two integrals to be evaluated.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Trigonometric and Logarithmic Integrals

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Problem 1 (page 1)

Deriving a trigonometric formula and differentiating a logarithmic expression, then using those results to evaluate two integrals.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Definite Integrals

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Problem 1 (page 1)

Two integrals to be evaluated.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Trigonometric Formulas and Identities

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(page 1)

A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differentiation Formulas: Polynomials, Products, Quotients

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.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Differentials and Indefinite Integration

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.

Instructor: Prof. David Jerison
Prior Knowledge: None