18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Fundamental Theorem of Calculus is presented and justified.

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

Statement and explanation of the two forms for the Fundamental Theorem of Calculus.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Using the Fundamental Theorem to evaluate an integral.

- Complete exam problem 5 on page 1
- Check solution to exam problem 5 on page 1

Six questions which involve finding areas under curves and evaluating definite integrals.

- Complete exam problem 3C–1 on page 22 to problem 3CC–6 on page 22
- Check solution to exam problems on page 40

General algorithm for evaluating integrals using the Fundamental Theorem of Calculus.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Statement and explanation of the First and Second Fundamental Theorems, with examples.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

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.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

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.

- Complete exam problem 4 on page 1
- Check solution to exam problem 4 on 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.

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

Four part question which involves finding critical points and values of a function which is defined in terms of an integral.

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

- Complete exam problem 10 on page 2
- Check solution to exam problem 10 on page 1