1. “In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.” - Hugo Rossi

2. 4.2 Area

3. Riemann Sum: the sum of the areas of approximating rectangles.

4. Definition of Area: *under the curve f(x) on the interval [a, b]

6. Ex 2: Let A be the area of the region that lies under the graph of f (x) = sin x between x = 0 and x = . Find an expression for A as a limit.

7. Summation Formulas Constant Series Constant Series

8. Summation Formulas Linear Series Linear Series

9. Summation Formulas Quadratic Series Quadratic Series

10. Summation Formulas Cubic Series Cubic Series

11. Ex 3: a) Evaluate the Riemann sum for f(x) = 2 – x 2 on [0, 2] w/ 4 subintervals using RHE. (find an approximate answer) b) Use the limit definition of the definite integral to find the area from part a. (find the exact answer)

12. 4.2 pg. 268 # 23 – 43 odds, # 47 – 53 odds, # 71 & 72