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VIDEO solution:Approximating areas Estimate the area of the region bounded by the graph of f(x)=x^2 2 and the x-axis on [0,2] in the following ways. a. Divide [0,2] into n=4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,2] into n=4 subintervals and approximate the area of the region using a midpoint Riemann sum. Illustrate the solution geometrically. c. Divide [0,2] into n=4 subintervals and approximate the area
VIDEO solution:Approximating areas Estimate the area of the regi…
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EXAMPLE 2: For the region under f(x) ≤ x² on [0, 2], show that the sum of the areas of the upper approximating rectangles approaches 40/3, that is, 40 lim Rn → 0.SOLUTION: Rn is the sum of the areas of the n rectangles in the figure. Each rectangle has a width of 2/n and the heights are the values of the function f(x) ≤ x² at the points 2/n, 4/n, 6/n, ..., 2n/n; that is, the heights are 5(2/n)², 5(4/n)², 5(6/n)², ..., 5(2n/n)². Thus,10 10 10 10 2nRn = (2/n)(5(2/n)²) (2/n)(5(4/n)²
EXAMPLE 2: For the region under f(x) ≤ x² on [0, 2], show that th…
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Calculus I and II Lecturer-21: The Area Under a Curve Approximation of areas with sums of rectangle areas. Right-endpoint, left-endpoint, and midpoint approximations; upper and lower sums (Part-01). Video credits to #selwyn_Hollis University of Houston Department of Mathematics. For further information https://online.math.uh.edu/HoustonACT/videocalculus/ https://www.casa.uh.edu/cwdrive/Viewer/flashplay.html?uf=21-area-H264__2530129a-0b65-468e-afd3-a1020a56af76.mp4 | Mathematical Muse
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