21) Find the number of compositions M needed so that the error of the integralS In(x + 2) dxis less than 10-8,using composite Simpson method.

Answered: 21) Find the number of compositions M…

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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21) Find the number of compositions M needed so that the error of the integral
S In(x + 2) dx
is less than 10-8,using composite Simpson method.

Expert Solution

Step 1

Simpson's rule can be used to approximate the value of the integration using numerical integration. The formula for the error in the composite Simpson's is $e r r o r = |\frac{h^{4}}{180} (b - a) \underset{ξ \in [a, b]}{m a x} f^{4} (ξ)|$ .

Here, h is the step size. The step size can be calculated using the formula $h = \frac{b - a}{n}$ .

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