Lecture Notes: Monday, November 9, 1998

 

Ninth Homework Assignment - for discussion at recitations Tuesday November 10, and Thursday November 12.

Chapter 6 Section 3 (Area and the Definite Integral)

Two problems:

Approximate solutions to both problems lead to the same Riemann sum. The limit of this Riemann sum as the partition of the interval from 0 to 10 gets finer and finer is a number called the Riemann integral of f(x) from 0 to 10.

Formal definition of definite integral.

Theorem: Continuous functions are integrable.

Area interpretation if f(x) changes sign.

Approximations using

Problem 6.3 #10.

After starting this problem by hand, we used MAPLE and "with(student)."

We also used right and left endpoints and saw how to use these estimates to get bounds on the integral .

 

MAPLE Demonstration #11 Please work through this demonstration.

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