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31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral (32 f(x) dx. x 0.0 0.4 0.8 1.2 1.6 f(x) x 2.0 2.4 2.8 3.2 6.8 6.5 6.3 6.4 6.9 f(x) 7.6 8.4 8.8 9.0 (b) If it is known that −4 ≤ ƒ"(x) ≤ 1 for all x, estimate the error involved in the approximation in part (a).

31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral (32 f(x) dx. x 0.0 0.4 0.8 1.2 1.6 f(x) x 2.0 2.4 2.8 3.2 6.8 6.5 6.3 6.4 6.9 f(x) 7.6 8.4 8.8 9.0 (b) If it is known that −4 ≤ ƒ"(x) ≤ 1 for all x, estimate the error involved in the approximation in part (a).

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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31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral (32 f(x) dx. x 0.0 0.4 0.8 1.2 1.6 f(x) 6.8 6.5 6.3 6.4 6.9 X 2.0 2.4 2.8 3.2 f(x) 7.6 8.4 8.8 9.0 (b) If it is known that -4 ≤ f"(x) < 1 for all x, estimate the error involved in the approximation in part (a).
Transcribed Image Text:31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral (32 f(x) dx. x 0.0 0.4 0.8 1.2 1.6 f(x) 6.8 6.5 6.3 6.4 6.9 X 2.0 2.4 2.8 3.2 f(x) 7.6 8.4 8.8 9.0 (b) If it is known that -4 ≤ f"(x) < 1 for all x, estimate the error involved in the approximation in part (a).
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