## Lecture Notes: Friday, November 13, 1998

Tenth Homework Assignment - for discussion at recitations on Tuesday November 17, Thursday November 19, and Tuesday, November 24. Because of the Thanksgiving holiday, students who normally attend recitation on Thursdays are welcome to choose a recitation to attend on Tuesday, November 24. This recitation will be devoted to Chapter 6. Our Exam #5 (Tuesday, December 1) will cover the course through Chapter 6.

### Chapter 6

We first reviewed the statement of the Fundamental Theorem of Calculus. In sketching the proof last time we found (text p 380) that the derivative of a definite integral with respect to its upper end point is the integrand evaluated at that upper end point. (d/dx)(int(f(t),t=a..x)) = f(x). This basic fact is equivalent to the Fundamental Theorem and is also often called the Fundamental Theorem of Calculus.

• Section 5 (Evaluating Definite Integrals)
• Properties of the Definite Integral (text p 384)
• Note especially property 5. It holds for any three numbers a,b,c.
• Section 6.5 #10. Substitution in the definite integral. Change of limits.
• Section 6.5 #32. Average value of a function. From a Riemann Sum.

MAPLE Demonstration #12.Please work through this demonstration.

Lecture Notes Directory

Course Guide