The estimation error is strangely obtained from Simpson's 1/3 rule... (2024)

Why do you insert C = 480 in the formula ?

And did you think about all the errors that arise because the function evaluation is imprecise and because you lose precision when summing the 960 values in the variable "int" ?

Maybe using advanced precision with vpa can help.

Oh I didn't know that.

I chose 480, which is the middle value between 0 and 960.

I didn't know to think about all the errors that occur due to loss of precision when summing 960 values ​​in variable "int".

I know this is really hard, but could you tell me about using advanced precision with vpa?

I didn't know to think about all the errors that occur due to loss of precision when summing 960 values in variable "int"

Plus the error in evaluating a polynomial with such small coefficients. You will have to go the symbolic way (see below).

syms a b c d e real

syms t real

f(t) = a*t^5 + b*t^4 + c*t^3 + d*t^2 + e*t;

s = 0;

i = -1/2;

while i < 959.5

i = i + 1;

tleft = i-1/2;

tmiddle = i;

tright = i+1/2;

fleft = f(tleft);

fmiddle = f(tmiddle);

fright = f(tright);

s = s + sym(1)/sym(6)*(fleft+sym(4)*fmiddle+fright);

end

s = simplify(s)

s_exact = int(f,t,0,960)

difference = s-s_exact

double(subs(difference,[a,b],[-1.93317553181561E-24,3.788630291530091e-21]))