2. a) Estimate the area bounded by the curve and the x-axis on [1, 6] usingthe 5 equal subintervals by finding:3The Left Riemann sum:The Right Riemann sum:b) Let R be the region bounded by the graph of f (x) = Vx and x-axis between x = 0 and x = 1. Sketch theregion. Approximate the area of R using a left Riemann sum with n=4 subintervals.c) Let R be the region bounded by the graph of f (x) = 2x – x² and x-axis between x = 0 and x = 2.Sketch the region. Approximate the area of R using a right Riemann sum with n=4 subintervals.

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Answered: 2. a) Estimate the area bounded by the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Estimate the area of the region bounded by the graph of f(x)=x +4 and the x-axis on [0,6] in the following ways. a. Divide [0,6] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,6] into n = 4 subintervals and approximate the area of the region using a right Riemann sum. Illustrate the solution geometrically. a. The left Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph of f and the rectangles used in the left Riemann sum. Choose the correct graph below. O A. 48- 7.5 X O B. 48- 0- 0 7.5 b. The right Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph of f and the rectangles used in the right Riemann sum. Choose the correct graph below. O A. Ay 48- مخملييملمم 7.5 LY O B. 48- 7.5 X X G O C. 48- OC. 48- 0 7.5 7.5 X ♫ E E
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2. a) Estimate the area bounded by the curve and the x-axis on [1, 6] using the 5 equal subintervals by finding: 3 The Left Riemann sum: The Right Riemann sum: