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

Click here to go to the next page

Send any comments or questions to: David Pleacher