5.1 Area.

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Presentation transcript:

5.1 Area

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

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

Definition of Area:

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

Ex 3: Determine a region whose area is equal to the given limit:

Ex 4: t: sec 5 10 15 20 25 v(t): ft/sec 31 35 43 47 46 Use the data to estimate the distance traveled from 0 to 25 seconds (use a right & left handed sum with 5 subintervals).

5.1 pg. 376 #1, 5, 11, 13, 15, 17, 18, 20

Summation Formulas Constant Series

Summation Formulas Linear Series

Summation Formulas Quadratic Series

Summation Formulas Cubic Series