“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.

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Presentation transcript:

“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

4.2 Area

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

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

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.

Summation Formulas Constant Series Constant Series

Summation Formulas Linear Series Linear Series

Summation Formulas Quadratic Series Quadratic Series

Summation Formulas Cubic Series Cubic Series

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)

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