Lesson #98
The Definite Integral and Area Under A Curve




Quote of the Day:

"But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not." -- Johann Bernoulli



Objectives:

The student will compute definite integrals.

The student will find the area under a curve by computing the definite integral.



1. Collect Homework.

2. Definition of the Definite Integral



3. Examples





4. Relationship of Area Under a Curve and the Definite Integral



Given the function above with the areas indicated, evaluate the integrals below:



5. Song about Area Under the Curve

6. Find the area under one arch of the sine curve.



7. Assignment
p. 394 (11a-d, 13a-d, 14a,b,c, 17)

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Send any comments or questions to: David Pleacher