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)

Lesson #98 The Definite Integral and Area Under A Curve

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