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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

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

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

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

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

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.

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

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

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete exam problem 4 on pages 6–7
- Check solution to exam problem 4 on pages 3–6

Computing the antiderivative of a fraction of two polynomials.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete exam problem 2 on page 3
- Check solution to exam problem 2 on pages 1–2

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Three integrals to be evaluated.

- Complete exam problem 9 on page 1
- Check solution to exam problem 9 on page 2
- Complete exam problem 3 on page 1
- Check solution to exam problem 3 on page 1

Two integrals to be evaluated.

- Complete exam problem 5a on page 2
- Check solution to exam problem 5a on page 2

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

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problem 1 on page 1
- Check solution to exam problem 1 on page 1

Two integrals to be evaluated.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problem 1 on page 1
- Check solution to exam problem 1 on page 1

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

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problem on page 1

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.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 1E-1 on page 4 to problems 1E-5 on page 5
- Check solution to exam problems on page 9

Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 3A–1 to 3A–3 on page 21
- Check solution to exam problems 3A–1 to 3A–3 on pages 37–9

Six questions which involve evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 5A–1 to 5A–6 on page 35
- Check solution to exam problems 5A–1 to 5A–6 on pages 69–71