The error term in Simpson\'s rule is O(h), or more precisely, when (a, b] is spl

Question

The error term in Simpson's rule is O(h), or more precisely, when (a, b] is split into n equal-sized subintervals and Simpson's rule is used for each subinterval, the accumulated error is bounded by: 180 la,b) where h=(b-a)/n. For the function f(x) = sin(x) and the integral fo,f(x)dx, what value of n will ensure that the 1. What value of n did you find? 2. It takes 3 function calls per subinterval for Simpson's rule. How many function calls are truncation error is no more than 10-12? (Use |f')| S 1.) needed by Simpson's for this n? 3. It takes 14 function calls to reach an error of size 10-12 for Julia's quadgk function. Which method uses fewer function calls? (Simpson's or quadgk)

Explanation / Answer

Here,

H=(b-a)

(b-a)/180

So,

Simpson rules

It show that square to variables

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