Approximate the following integral using the Simpson's Rule with n=4a) Provide an exact answer for your approximation and a decimal answer rounded to 24.decimal places. b) Given that max f(0(x) =3/2on the interval, determine the error16bound on your approximation.4|xVx+ 2dx

Answered: Approximate the following integral…

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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Question

Approximate the following integral using the Simpson's Rule with n=4
a) Provide an exact answer for your approximation and a decimal answer rounded to 2
4.
decimal places. b) Given that max f(0(x) =
3/2
on the interval, determine the error
16
bound on your approximation.
4
|xVx+ 2dx

Expert Solution

Step 1

Consider the provided question,

We have to find the approximate value of integral using the Simpson's rule with n = 4,

$Given that, \int_{0}^{4} x \sqrt{x + 2} d x L e t f (x) = x \sqrt{x + 2} H e r e, a = 0, b = 4, n = 4 Step size (h) = \frac{b - a}{n} = \frac{4 - 0}{4} = 1$

The table according to the obtained interval is constructed as,

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