Explanation Suffices to estimate S 4 for ∫ 3 5 x 2 d x , a s ∫ 3 5 ( 9 − x 2 ) d x = 18 − ∫ 3 5 x 2 d x Simpson’s rule is an estimate for the value of the definite integral ∫ a = x 0 b = x N f ( x ) d x , which is the area under the curve y = f ( x ) , between a = x 0 a n d b = x N ,N denoting the number of intervals into which the interval [a, b] is divided. The area is approximated as the sum of the areas under parabolas, resulting in a finite sum using the function values of f(x) at the division points. The case for N = 6 is illustrated in the adjoining figure: Formula used: Let N (an even positive integer) be given. Let the interval [a, b] be equally divided into N subintervals at the points x 0 = a , x 1 = a + h , x 2 = a + 2 h , ..... , x N − 1 = a + ( N − 1 ) h , x N = a + N h = b (1) With h = b − a N (2) Let y 0 = f ( x 0 ) = f ( a ) , y 1 = f ( x 1 ) , .... y i = f ( x i ) , ... y N = f ( x N ) = f ( b ) (3) (In other words , y i is the function value at the i th division point x i ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 8.8, Problem 17E

To determine

The approximate value $S_{6}$ of $\int_{0}^{3} \frac{1}{x^{4} + 1} d x$ , using Simpson’s rule, with $N = 6$

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Chapter 8.8, Problem 16E

Chapter 8.8, Problem 18E

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Chapter 8 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The approximate value S 6 of ∫ 0 3 1 x 4 + 1 d x , using Simpson’s rule, with N = 6

Solution Summary: The author explains Simpson's rule, which is an estimate for the value of the definite integral a = x 0 b = N f

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The approximate value $S_{6}$ of $\int_{0}^{3} \frac{1}{x^{4} + 1} d x$ , using Simpson’s rule, with $N = 6$

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The approximate value S 6 of ∫ 0 3 1 x 4 + 1 d x , using Simpson’s rule, with N = 6

Solution Summary: The author explains Simpson's rule, which is an estimate for the value of the definite integral a = x 0 b = N f

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The approximate value S6of ∫031x4+1dx, using Simpson’s rule, with N=6

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The approximate value $S_{6}$ of $\int_{0}^{3} \frac{1}{x^{4} + 1} d x$ , using Simpson’s rule, with $N = 6$