ЧМ ЛР5

function I = Simpson(x)

I = 0;

h = x(2) - x(1);

for i = 2:1:length(x)

I = I + (f(x(i))+4*f(x(i)-h/2)+f(x(i-1)))*h/6;

end

end

function I = Trapez(x)

I = 0;

h = x(2) - x(1);

for i = 2:1:length(x)

I = I + (f(x(i))+f(x(i-1)))*h/2;

end

end

>> x = 0:0.1:1;

function f = f(x)

f = x^3;

end

>> Trapez(x)

ans = 0.2525

>> e = abs(1/4 - ans)

e = 0.0025

>> Simpson(x)

ans = 0.2500

>> e = abs(1/4 - ans)

e = 0

function f = f(x)

f = x^2;

end

>> Trapez(x)

ans = 0.3350

>> e = abs(1/3 - ans)

e = 0.0017

>> Simpson(x)

ans = 0.3333

>> e = abs(1/3 - ans)

e = 5.5511e-17

function f = f(x)

f = x/2;

end

>> Trapez(x)

ans = 0.2500

>> e = abs(1/4 - ans)

e = 5.5511e-17

>> Simpson(x)

ans = 0.2500

>> e = abs(1/4 - ans)

e = 0

function f = f(x)

f = 1/(1+x^2);

end

>> x = 0:(10^-6):1;

>> Trapez(x)

ans = 0.7854

>> PI = ans*4

PI = 3.1416

>> e = abs(pi-PI)

e = 7.5495e-14

>> Simpson(x)

ans = 0.7854

>> PI = ans*4

PI = 3.1416

>> e = abs(pi-PI)

e = 1.0170e-13

function f = f(x)

f = 1/(1+x^2);

end

>> x = 0:(10^-6):1;

function I = Trapez(x)

I = 0;

h = x(2) - x(1);

for i = 2:1:length(x)

I = I + (f(x(i))+f(x(i-1)))*h/2;

end

end

>> Trapez(x)

>> s = Trapez(x)

s = 0.7854

>> PI = ans*4

PI = 3.1416

>> e = abs(pi-PI)

e = 7.5495e-14

function I = Trapez(x)

I = 0;

h = x(2) - x(1);

for i = 2:1:length(x)

I = I + (f(x(i)-h/2)+f(x(i-1)))*h/4 + (f(x(i))+f(x(i)-h/2))*h/4;

end

end

>> p = Trapez(x)

p = 0.7854

>> e = abs(p-s)

e = 3.4417e-15

>> PI = p*4

PI = 3.1416

>> E = abs(PI-pi)

E = 8.9262e-14