#498 new
James McCoy

Gauss formulas

Reported by James McCoy | June 5th, 2018 @ 06:53 AM

Let's rewrite the estimate of the error of Gauss formulas:
procedure Simp(n1:integer;var s:real);
i:integer; h:real; s1,s2:real; begin
h:=(b-a)/n1; s1:=0; s2:=0; for i:=1 to n1-1 do if i mod 2=0 then s1:=s1+f(a+i*h) else s2:=s2+f(a+i*h); s:=h/3*(f(a)+f(b)+2*s2+4*s1); end;{end Simp}

Let the integral function be continuous. Then, according to the Weierstrass theorem (taken from hireessaywriter.org students' database), for any one there exists a polynomial, for which it follows that, then, for any continuous function, the error of the Gaussian formulas with
Task1. Let it be an integrated function. Prove that for Gaussian formulas.

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