## 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:

- 1. Area under the graph of a the function f(x) = x^2 and above
the x-axis, between x=0 and x=10.
- 2. Rod of density x along x-axis from 0 to 10. Moment of
inertia about x=0.

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

- midpoints
- left endpoints
- right endpoints

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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