18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

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

Using the Fundamental Theorem to evaluate an integral.

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

Eight questions which involve functions defined with integrals, and these functions must be described, evaluated, or used to prove some statement.

- Complete practice problem 3D–1 to problem 3D–8 on page 23
- Check solution to practice problems on pages 41–2

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Fundamental Theorem of Calculus is presented and justified.

Using the Fundamental Theorem to evaluate the derivative of a function which is defined in terms of an integral.

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

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.

Explanation of the implications and applications of the Second Fundamental Theorem, including an example.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Using the Second Fundamental Theorem to define the natural logarithm function and the error function, including diagrams and 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, inluding 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