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# Lecture30 - Math 121 Lecture 30 6.2 Areas and Riemann Sums Area Under a Graph Riemann Sums to Approximate Areas(Midpoints Riemann Sums to

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§ 6.2 Areas and Riemann Sums Math 121 Lecture 30 ! Area Under a Graph ! Riemann Sums to Approximate Areas (Midpoints) ! Riemann Sums to Approximate Areas (Left Endpoints) ! Applications of Approximating Areas

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Definition Example Area Under the Graph of f ( x ) from a to b : An example of this is shown to the right In this section we will learn to estimate the area under the graph of f ( x ) from x = a to x = b by dividing up the interval into partitions (or subintervals), each one having width where n = the number of partitions that will be constructed. In the example below, n = 4. A Riemann Sum is the sum of the areas of the rectangles generated above.
Use a Riemann sum to approximate the area under the graph f ( x ) on the given interval using midpoints of the subintervals The partition of -2 ! x ! 2 with n = 4 is shown below. The length of each subinterval is -2 2 x 1 x 2 x 3 x 4 Observe the first midpoint is units from the left endpoint, and the midpoints themselves are units apart. The first midpoint is

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Lecture30 - Math 121 Lecture 30 6.2 Areas and Riemann Sums Area Under a Graph Riemann Sums to Approximate Areas(Midpoints Riemann Sums to

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