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Evaluate the Riemann sum for f(x) = 4 -x, 2s x s 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; - 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where %3D i = 1 Xo, X1, X2, X3, X4 and X5 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 2 Step 2 We wish to find L6 (2)[f(x,) + f(xq) + f(x2) + f(x3) + f(x4) + %3D Since xo, X4, X, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following.

Evaluate the Riemann sum for f(x) = 4 -x, 2s x s 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; - 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where %3D i = 1 Xo, X1, X2, X3, X4 and X5 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 2 Step 2 We wish to find L6 (2)[f(x,) + f(xq) + f(x2) + f(x3) + f(x4) + %3D Since xo, X4, X, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Evaluate the Riemann sum for f(x) = 4 -x, 2 s xs 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; _ 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where i = 1 Xo, X1, X2, X3, X4 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. and X5 Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 Step 2 We wish to find L6 (2)[f{x,) + f(xq) + f(x2) + f(x3) + f(x4) + f(xg)]. %3D Since x, X4, X,, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following. Xo = 2 X, = X2 = 6. 8. X3
Transcribed Image Text:Evaluate the Riemann sum for f(x) = 4 -x, 2 s xs 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; _ 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where i = 1 Xo, X1, X2, X3, X4 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. and X5 Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 Step 2 We wish to find L6 (2)[f{x,) + f(xq) + f(x2) + f(x3) + f(x4) + f(xg)]. %3D Since x, X4, X,, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following. Xo = 2 X, = X2 = 6. 8. X3
X3 = 8 V X 4 10 %3D 10 X5 = 12 %3D 12 Step 3 Using f(x) = 4 – we have the following. L6 = (2)[f(2) + f(4) + f(6) + f(8) + f(10) + f(12)] %3D = 2 3 + (2) + (1) + (0) + (-1) + (-2
Transcribed Image Text:X3 = 8 V X 4 10 %3D 10 X5 = 12 %3D 12 Step 3 Using f(x) = 4 – we have the following. L6 = (2)[f(2) + f(4) + f(6) + f(8) + f(10) + f(12)] %3D = 2 3 + (2) + (1) + (0) + (-1) + (-2
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