Use the error formulas to estimate the errors in approximating the integral, wit

Question

Use the error formulas to estimate the errors in approximating the integral, with n = 4. (Round your answers to two decimal places.)

I need the solution for Simpson's rule please please show me what to do

Explanation / Answer

Errror= |exact - numerical |= (b-a)*M.h^4/180 where M= |f ' ' ' ' (x) | f(x) = 2x^3 f ' = 6x^2 f ' ' = 12x f ' ' ' = 12 ==> f ' ' ' '(x) = 0 ==> M= 0 HENCE Errror= |exact - numerical |= (b-a)*M.h^4/180 = 0 numerical result gives same as exact value exact = int_{3}^{4} 2x^3 dx = 175 / 2 = 87.5 numerical : a=3 b=4 n=4 h=(b-a)/n= (4-3)/4 = 1/4 simpson's= (h/3) ( f(3) + 4 f(3+ 1/4) + 2 f(3+ 2/4) + 4/f(3+ 3/4) + f(3+ 4/4) ) = (1/4)(1/3) ( f(3) + 4 f(3+ 1/4) + 2 f(3+ 2/4) + 4 f(3+ 3/4) + f(3+ 4/4) ) =87.5 errorr = 0.0

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