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Determine the values of n and h required to approximate I e 2xsin3xdx Jo to within l()~4

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 11 Chapter 4.4

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 11

Determine the values of n and h required to approximate I e 2xsin3xdx Jo to within l()~4 . Use a. Composite Trapezoidal rule. b. Composite Simpson's rule. c. Composite Midpoint rule.

Step-by-Step Solution:

Integrating any rational function Ratio of polynomials: by expressing the function 3 2 2 x −1 = (x−1)(x +1) = x(x−1) (+−1)(x +1)  x −1 x(x +1) x(x +1) x(x +1) x−1 x−1 x 1 1  ¿ 2 + = 2 − 2 +1− x +1 x x +1 x +1 x Decompose any rational function P(x) R(x)= =G x)+ f1x)+ f2x +… f kx) Q( ) f (x) A Bx+c i {(ax+b ) (p x +qx+r)m} Example 3 2 x +x +x−1 ∫ 2 x +2 x+2 Step 1 if numerator is of higher degree than denominator Long division Multiple everything by x here x+1 ∫ xdx−∫dx+ ∫ 2 x +2x+2 2 letu=x +2x+2 du= 2x+2 )dx 1 du= (+1 d) 2

Step 2 of 1

Chapter 4.4, Problem 11 is Solved
Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Determine the values of n and h required to approximate I e 2xsin3xdx Jo to within l()~4