Simpsons rule for the numerical evaluation of an integral is where n is an even number The global truncation error is If f(x) ln cosh x and a 0, b 0 5, show that f (4) (x) 4) If f(x) is tabulated to 4dp, show that the accumulated rounding error using the formula is less than 1 40 000, and find n su...

fx ln cosh x f xtanh x fx sech x fx 2 sech x tan x f4 x 4 sech x tanh x 2 sec ...

Simpsons rule for the numerical evaluation of an integral is where n is an even number. The

Question:

Simpson’s rule for the numerical evaluation of an integral is

S f(x)dx= b-a n -(fo+ 4f +2f+.... + 2 fn-2 + 4f-1+ fn)

where n is an even number. The global truncation error is

(b-a)5 180n* -f) (c), with a

If f(x) = ln cosh x and a = 0, b = 0.5, show that |f⁽⁴⁾(x)| 4). If f(x) is tabulated to 4dp, show that the accumulated rounding error using the formula is less than 1/40 000, and find n such that, using the formula, the integral ∫₀^0.5 ln cosh x dx would be evaluated correctly to 4d

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