Use Simpson's rule with n = 6 to approximate:-dxGive the answer correct to 4 decimal places:Simpson's Rule : * f(x)dx ≈ [f(x0) + 4f(x;) + 2f(x ₂) + 4 f(x 3) +wheren is even and Ax =b-an+ 2f(x₁-2) + 4f(xn-1) + f(x₂)]

Given information:Provided integral isThe number of sub-intervals is given as .To find:Approximate…

Answered: Use Simpson's rule with n = 6 to…

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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Related questions

Question

Use Simpson's rule with n = 6 to approximate:
-dx
Give the answer correct to 4 decimal places:
Simpson's Rule : * f(x)dx ≈ [f(x0) + 4f(x;) + 2f(x ₂) + 4 f(x 3) +
wheren is even and Ax =
b-a
n
+ 2f(x₁-2) + 4f(xn-1) + f(x₂)]

Expert Solution

Step 1: Introduction.

Given information:

Provided integral is $integral subscript 1 superscript 4 1 over x squared d x$

The number of sub-intervals is given as $n equals 6$ .

To find:

Approximate value of the integral using Simpson's rule.

Formula used:

$integral subscript a superscript b f left parenthesis x right parenthesis d x almost equal to fraction numerator increment x over denominator 3 end fraction open square brackets open square brackets f open parentheses x subscript 0 close parentheses plus f open parentheses x subscript n close parentheses close square brackets plus 2 open square brackets f open parentheses x subscript 2 close parentheses plus f open parentheses x subscript 4 close parentheses plus... plus f open parentheses x subscript n minus 2 end subscript close parentheses close square brackets plus 4 open square brackets f open parentheses x subscript 1 close parentheses plus f open parentheses x subscript 3 close parentheses plus... plus f open parentheses x subscript n minus 1 end subscript close parentheses close square brackets close square brackets$

Where,

$a$ and $b$ are the lower and upper limits of integration.

$n$ is the number of sub intervals

$increment x$ is the width of each sub interval, given by $increment x equals fraction numerator b minus a over denominator n end fraction$ .