Explanation Given information: f ( x ) = x 2 , N = 4 , interval [ 1 , 3 ] . Formula used: S N = Δ x 3 ( f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + ....... + 2 f ( x N − 2 ) + 4 f ( x N − 1 ) + f ( x N ) ) , w h e r e , Δ x = b − a N a n d x i = x i − 1 + Δ x , 1 ≤ i ≤ N { x 0 = a a n d x N = b } Calculation: For interval [ 1 , 3 ] a n d N = 4 , Δ x = 3 − 1 4 = 1 2 So, the points are x 0 = 1 , x 1 = 1 + 1 2 = 3 2 , x 2 = 3 2 + 1 2 = 2 , x 3 = 2 + 1 2 = 5 2 , x 4 = 5 2 + 1 2 = 3 S 4 = 1 3 ⋅ 2 ( f ( x 0 ) + 4 f ( x 1 )

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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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 7.8, Problem 13E

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To calculate:

SN of x2 over interval [1,3] and N=4.

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Chapter 7.8, Problem 12E

Chapter 7.8, Problem 14E

Chapter 7 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY

S N of x 2 over interval [ 1 , 3 ] a n d N = 4 .

Solution Summary: The author explains how to calculate S_N over interval [1,3]

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To calculate:

SN of x2 over interval [1,3] and N=4.

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Chapter 7 Solutions

S N of x 2 over interval [ 1 , 3 ] a n d N = 4 .

Solution Summary: The author explains how to calculate S_N over interval [1,3]

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Videos

To calculate: SN of x2 over interval [1,3] and N=4.

Want to see the full answer?

Chapter 7 Solutions

To calculate:

SN of x2 over interval [1,3] and N=4.