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1. Evaluate the Riemann sum for f(x) = x - 1,-6

1. Evaluate the Riemann sum for f(x) = x - 1,-6

Advanced Engineering Mathematics
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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1. Evaluate the Riemann sum for f(x) = x - 1,-6 <x 4, with five subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what the Riemann sum represents. 2. If f(x) = cos x 0 <x< 3T/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Give your answer correct to six decimal places.) What does the Riemann sum represent? Illustrate with a diagram. 3. If f(x) = x² – 4,0 <x<3, evaluate the Riemann sum with 6, taking the sample points to be midpoints. What does the Riemann sum represent? Illustrate with a diagram. n = 4. (a) Evaluate the Riemann sum for f(x) 1/x, 1 <x< 2, with four terms, taking the sample points to be right end- points. (Give your answer correct to six decimal places.) Explain what the Riemann sum represents with the aid of a sketch. (b) Repeat part (a) with midpoints as the sample points. 5. The graph of a function f is given. Estimate Jo" F(x) dx using five subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. YA 1
Transcribed Image Text:1. Evaluate the Riemann sum for f(x) = x - 1,-6 <x 4, with five subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what the Riemann sum represents. 2. If f(x) = cos x 0 <x< 3T/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Give your answer correct to six decimal places.) What does the Riemann sum represent? Illustrate with a diagram. 3. If f(x) = x² – 4,0 <x<3, evaluate the Riemann sum with 6, taking the sample points to be midpoints. What does the Riemann sum represent? Illustrate with a diagram. n = 4. (a) Evaluate the Riemann sum for f(x) 1/x, 1 <x< 2, with four terms, taking the sample points to be right end- points. (Give your answer correct to six decimal places.) Explain what the Riemann sum represents with the aid of a sketch. (b) Repeat part (a) with midpoints as the sample points. 5. The graph of a function f is given. Estimate Jo" F(x) dx using five subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints. YA 1
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