clc;

close all;

fun = 'sin(x)';

a = -pi; %poczatek przedzialu

b = pi; %koniec przedzialu

skok = 0.5; %krok

f = inline(fun);

vx = a : skok/110 : b;

vy = f(vx);

plot(vx, vy, 'g');

hold on;

lx = [a];

ly = [0];

calka = 0;

for x = a : skok : b

if(x+skok > b)

skok = b-x;

end

calka = calka + skok*f(x+skok/2);

lx = [lx, x, x+skok, x+skok];

ly = [ly, f(x+skok/2), f(x+skok/2), 0];

end

line ([a b], [0 0]);

calka

line(lx, ly);

axis ([a b min(vy) - 0.01 max(vy)+ 0.01]);

TITLE ('metoda prostakatna');

%paraboli
clc

clear all

close all

a=-pi;

b=pi;

x=a:0.01:b;

f=inline('sin(x)');

y=f(x);

plot(x,y);

hold on

n=100;

h=(b-a)/n

x1=linspace(a,b,n);

y1=f(x1);

I=h/3*(y1(1)+y1(n)+4*sum(y1(1:2:n-1))+2*sum(y1(2:2:n-2)))

for(i=1:n)

line([x1(i),x1(i)],[0,y1(i)]);

end

clc

clear all

close all

a=-pi;

b=pi;

n=100;

f=inline('sin(x)');

x=a:0.01:b;

y=f(x);

plot(x,y);

hold on

d=min(y);

g=max(y);

counto=0;

countb=0;

for i=1:n

xs=rand*(b-a)+a;

ys=rand*(g-d)+d;

if(ys>0)

if(ys<f(xs))

counto=counto+1;

plot(xs,ys,'g *');

else

plot(xs,ys,'r *');

end

elseif(ys<0)

if(ys>f(xs))

countb=countb+1;

plot(xs,ys,'g *');

else

plot(xs,ys,'r *');

end

end

end

I=(counto-countb)/n*(b-a)*(g-d)

%prostokatow

clc

clear all

close all

a=-pi;

b=pi;

x=a:0.01:b;

f=inline('sin(x)');

y=f(x);

plot(x,y);

hold on

n=100;

h=(b-a)/n

x1=linspace(a,b,n);

y1=f(x1);

x1

I=h*(sum(y1)-f(b))

for(i=1:n)

line([x1(i),x1(i)],[0,y1(i)]);

end

%trapezow

clc

clear all

close all

a=-pi;

b=pi;

x=a:0.01:b;

f=inline('sin(x)');

y=f(x);

plot(x,y);

hold on

n=100;

h=(b-a)/n

x1=linspace(a,b,n);

y1=f(x1);

I=h*((y1(1)+y1(n)/2)+sum(y1)-y1(1)-y1(n))

for(i=1:n)

line([x1(i),x1(i)],[0,y1(i)]);

end

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