$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z1
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

format long;
clc
clear all;
syms x;
f=0.5*x^4 + x^2 -1;
pp=0.3;
pk=1.5;
eps=0.001;
fpr=diff(f,2);

kr=(pk-pp)/100;
for i=1:101,
    tmp(i,1)=subs(fpr,(pp+((i-1)*kr)));
end
M2=max(tmp);

h=sqrt((12*eps)/((pk-pp)*M2));
n=(pk-pp)/h;
n=floor(n);
h=(pk-pp)/n;

wyn=subs(f,pp)/2;
for i=1:(n-1),
    wyn=wyn+subs(f,(pp+(i*h)));
end
wyn=wyn+(subs(f,(pp+(n*h)))/2);
wyn=wyn*h

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z1 - inne
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

format long;
clc
clear all;
syms x;
f=0.5*x^4 + x^2 -1;
pp=0.3;
pk=1.5;
eps=0.001;
fpr=diff(f,2);

dx=(pk-pp)/100;
for i=1:101,
    xi(i,1)=(pp+((i/100)*(pk-pp)));
end
M2=max(xi);
for i=1:101,
    fi(i,1)=subs(f,(xi(i,1)))
end
for i=2:100,
    Px(i,1)=((f(i-1,1)+f(i,1))/2)*dx
end

P=0;
for i=1:101,
    S=P+Px(i,1)
end

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z2
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

format long
clc
clear all;
syms x;
f=0.5*x^4 + x^2 -1;
pp=0.3;
pk=1.5;
eps=0.0001;
fpr=diff(f,4);

kr=(pk-pp)/100;
for i=1:101,
    tmp(i,1)=subs(fpr,(pp+((i-1)*kr)));
end
M4=max(tmp);

h=sqrt(sqrt((180*eps)/((pk-pp)*M4)));
n=(pk-pp)/h;
n=floor(n);
h=(pk-pp)/n;

t=subs(f,pp)+subs(f,(pk));
for i=1:(n-1),
    t=t+2*subs(f,(pp+(i*h)));
end
for i=1:n,
    ti=((pp+((i-1)*h))+(pp+(i*h)))/2;
    t=t+4*subs(f,ti);
end

wyn=((pk-pp)/(6*n))*t

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z2a
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

clc
clear all
syms x;
f=0.5*x^4 + x^2 -1;
a=0.3;
b=1.5;
e=0.0001;
M=12;
h=((180*e)/((b-a)*M))^(1/4);
n=ceil((b-a)/h);
if mod(n,2)==1
    n=n+1;
end
n=6;
h=(b-a)/n;
calka=0;
j=a;
for i=1:n+1
    if i==1 || i==n+1
        calka=calka+subs(f,x,j);
    elseif mod(i,2)==0
        calka=calka+4*subs(f,x,j);
    else
        calka=calka+2*subs(f,x,j);
    end
    j=j+h;
end
calka=calka*(h/3)
%int(f,a,b)

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z3
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

format long;
clc
clear all;
syms x;
f=0.5*x^4 + x^2 -1;
pp=0.3;
pk=1.5;
eps=0.001;
h=sqrt(eps);
wyk=1;
iter=0;

while wyk==1,
    iter=iter+1;

    n=ceil((pk-pp)/h);
    h=(pk-pp)/n;
    h2=h/2;
    wyn1=subs(f,pp)/2;
    for i=1:(n-1),
        wyn1=wyn1+subs(f,(pp+(i*h)));
    end
    wyn1=wyn1+(subs(f,(pp+(n*h)))/2);
    wyn1=wyn1*h;

    n=ceil((pk-pp)/h2);
    h2=(pk-pp)/n;
    wyn2=subs(f,pp)/2;
    for i=1:(n-1),
        wyn2=wyn2+subs(f,(pp+(i*h2)));
    end
    wyn2=wyn2+(subs(f,(pp+(n*h2)))/2);
    wyn2=wyn2*h2;

    if(abs(wyn2-wyn1)<eps) wyk=0;
    else
        h=h/2;
    end
end

wyn1
wyn2
iter
n=(pk-pp)/h2

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Z4
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

format long;
clc
clear all;
syms x;
f=0.5*x^4 + x^2 -1;
pp=0.3;
pk=1.5;
eps=0.001;
h=sqrt(sqrt(eps));
wyk=1;
iter=0;

while wyk==1,
    iter=iter+1;

    n=ceil((pk-pp)/h);
    h=(pk-pp)/n;
    h2=h/2;
    t=subs(f,pp)+subs(f,(pk));
    for i=1:(n-1),
        t=t+2*subs(f,(pp+(i*h)));
    end
    for i=1:n,
        ti=((pp+((i-1)*h))+(pp+(i*h)))/2;
        t=t+4*subs(f,ti);
    end

    wyn1=((pk-pp)/(6*n))*t;

    n=ceil((pk-pp)/h2);
    h2=(pk-pp)/n;
    t=subs(f,pp)+subs(f,(pk));
    for i=1:(n-1),
        t=t+2*subs(f,(pp+(i*h2)));
    end
    for i=1:n,
        ti=((pp+((i-1)*h2))+(pp+(i*h2)))/2;
        t=t+4*subs(f,ti);
    end

    wyn2=((pk-pp)/(6*n))*t;

    if(abs(wyn2-wyn1)<eps) wyk=0;
    else
        h=h/2;
    end
end

wyn1
wyn2
iter
n=(pk-pp)/h2