## 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.

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