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I = f(x)dx a gives the error b - a E = f"(4). 12 Suppose 2+ 2x – e f"(x) = a = 0.51, b = 1.0. What values of n and h should be used to approximate I to within 0.00001? (b) Consider the integral So f(x)dx for the function 1 f(x) = -2e + 2x 4 120 Approximate I using the Composite trapezoidal rule with N = 4. (c) Use the Composite Simpson's rule with N = part (b) and compare the outcomes for the two methods given that the exact solution is Ieract = -0.21563. 4 to approximate the integral in

I = f(x)dx a gives the error b - a E = f"(4). 12 Suppose 2+ 2x – e f"(x) = a = 0.51, b = 1.0. What values of n and h should be used to approximate I to within 0.00001? (b) Consider the integral So f(x)dx for the function 1 f(x) = -2e + 2x 4 120 Approximate I using the Composite trapezoidal rule with N = 4. (c) Use the Composite Simpson's rule with N = part (b) and compare the outcomes for the two methods given that the exact solution is Ieract = -0.21563. 4 to approximate the integral in

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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(a) The Composite Trapezoidal Rule applied to the integral | f(x)dr I = gives the error b – E = – 12 -a h³ f" (µ). Suppose 2+ 2x et a = 0.51, b = 1.0. - f"(x) 3 What values of n and h should be used to approximate I to within 0.00001? (b) Consider the integral I = f f(x)dx for the function x4 f (x) = -2e-ª + 4 1 -x³ + 2x 120 Approximate I using the Composite trapezoidal rule with N = 4. (c) Use the Composite Simpson's rule with N part (b) and compare the outcomes for the two methods given that the exact solution is Iexact = 4 to approximate the integral in = -0.21563.
Transcribed Image Text:(a) The Composite Trapezoidal Rule applied to the integral | f(x)dr I = gives the error b – E = – 12 -a h³ f" (µ). Suppose 2+ 2x et a = 0.51, b = 1.0. - f"(x) 3 What values of n and h should be used to approximate I to within 0.00001? (b) Consider the integral I = f f(x)dx for the function x4 f (x) = -2e-ª + 4 1 -x³ + 2x 120 Approximate I using the Composite trapezoidal rule with N = 4. (c) Use the Composite Simpson's rule with N part (b) and compare the outcomes for the two methods given that the exact solution is Iexact = 4 to approximate the integral in = -0.21563.
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