Shortcut for Simpson’s Rule Using the notation of the text, prove that for n ≥ 1.

Problem 60AE

Shortcut for Simpson’s Rule Using the notation of the text, prove that Solution:Step 1<img src="https://chart.googleapis.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cleft%28%7BUsing%5C+h%3D%5Cfrac%7Bb-a%7D%7B2n%7D%7D%5Cright%29">

We write the formula for different approximation methods as follows,Trapezoid Rule approximation

Trapezoid Rule approximation

Simpson’s Rule approximation S(2n) =

Step 2Finding the value of using the above approximations methods, we get = = S(2n)

Hence, it is proved that .