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Riemann Sums as Estimates for Definite Integrals

November 8th, 2017. Riemann Sums as Estimates for Definite Integrals. Riemann Sums.

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Riemann Sums as Estimates for Definite Integrals

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  1. November 8th, 2017 Riemann Sums as Estimates for Definite Integrals

  2. Riemann Sums *A Riemann Sum is the sum of the areas of a finite number of rectangles that can be used to approximate a definite integral. The Left Riemann Sum uses rectangles whose height is determined by the left endpoint of the rectangle, whereas the Right Riemann Sum uses the right endpoint and the Midpoint Riemann Sum uses the midpoint.

  3. Ex. 1: Approximate by using a • (a) left Riemann sum with 4 equal subintervals • (b) right Riemann sum with 4 equal subintervals • (c) midpoint Riemann sum with 4 equal subintervals • Then, determine which of these gives the largest overestimate of the integral and the smallest underestimate of the integral.

  4. Ex. 2: The table above gives the velocity in miles per hour of a car traveling for t hours. Approximate the total distance traveled by the car using a • (a) left Riemann sum • (b) right Riemann sum • (c) midpoint Riemann sum

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