Lesson #94 Exact Area Under A Curve


Quote of the Day:
"Mathematics is not a deductive science — that's a cliché.  
   When you try to prove a theorem, you don't just list the 
   hypotheses, and then start to reason.  What you do is 
   trial and error, experimentation, guesswork."  
   -- Paul Halmos

Objectives:
The student will determine the area under a curve by 
   summing up rectangles and then taking a limit.

1. Collect Homework.

2. To determine the exact area under a curve, examine the
   diagrams below:

        

        

        

    Notice, as we increase the number of rectangles, we 
    get closer to the exact area under the curve.

        

3.Example

        

        

        

4. Example

        
     
5. Top Ten PickUp Lines (Look at #2 on the List)

6. Song Lyrics -- "Failing My Calculus"

7. Song about Riemann Sums
 
8. Riemann Sums in Visual Calculus

9. Assignment
     p. 384 (31abc, 33abc)

     Find exact area under y = 4x from x = 0 to x = 2 

     Find exact area under y = x² from x = 0 to x = 2
Lesson #94 Exact Area Under A Curve

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