Oʻzbekiston respublikasi axborot texnologiyalari va kommunikatsiyalarini rivojlantirish vazirligi muhammad al-xorazmiy nomidagi toshkent axborot texnologiyalari universiteti laboratoriya ishi Fan: Algoritmlarni loyihalash Guruh : cal010-L1

1) To’g’ri to’rtburchak usuli:


Algoritm



Boshlash



double s=0,x,f,h,a=exp,b=2*exp,n;



h=(b-a)/n



for(int i=1;i




x=a+h*i+h/2


F=ln(x-1)^2



s+=f



Cout<


Tamom

#include

using namespace std;
int main(){
double s=0,x,f,h,a=exp,b=2*exp,n;
cin>>n;
h=(b-a)/n;
for(int i=1;i<=n;i++){
x=a+h*i+h/2;
f=ln(x-1)*ln(x-1);
s+=f;
if(i%10==0){
cout< cout< cout< cout< }
}
cout< cout<}



2) Trapetsiya usuli:
Algoritm



Boshlash



double s=0,x,f,h,a=exp,b=2*exp,n;



h=(b-a)/n



for(int i=1;i




x=a+h*i+h/2


f=ln(x-1)^2



s+=f



Cout<


Tamom

#include

using namespace std;
int main(){
double s=0,x,f,h,a=exp,b=2*exp,n;
cin>>n;
h=(b-a)/n;
for(int i=1;i x=a+h*i+h/2;
f =ln(x-1)^2;
s+=f;
if(i%10==0){
cout< cout< cout< cout< }
}
cout< cout<}


3) Simpson usuli
Algoritm



Boshlash



double s=0,x,f,h,a=0,b=0.5,n;



h=(b-a)/n



s=sqrt((1+a)/(1-a))+sqrt((1+b)/(1-b));



for(int i=1;i




x=a+h*i+h/2


f=ln(x-1)^2



s+=f*4



for(int i=2;i




x=a+h*i+h/2


f=ln(x-1)^2



s+=f*2



Cout<


Tamom

#include

using namespace std;
int main(){
double s,x,f,h,a=0,b=0.5,n;
cin>>n;
h=(b-a)/n;
s=sqrt((1+a)/(1-a))+sqrt((1+b)/(1-b));
for(int i=1;i x=a+h*i+h/2;
f=ln(x-1)^2;
s+=f*4;
if(i%10==0){
cout< cout< cout< cout< }
}

for(int i=2;i x=a+h*i+h/2;
f= ln(x-1)^2;
s+=f*2;
if(i%10==0){
cout< cout< cout< cout< }
}
cout< cout<}

n	10	20	30	40	50	60	70	80	90	100	Integral qiymat
To’rtburchaklar usuli
	0.0525	0.1025	0.1525	0.2025	0.2525	0.3025	0.3525	0.4025	0.4525	0.5025
f(x(i))/y(i)	1.0539	1.1083	1.1661	1.2279	1.2944	1.3665	1.4452	1.532	1.6287	1.7378
h*(f(x))	0.00526	0.0055	0.0058	0.0061	0.0064	0.0068	0.0072	0.0076	0.0081	0.0086
Trapetsiya usuli
	0.0525	0.1025	0.1525	0.2025	0.2525	0.3025	0.3525	0.4025	0.4525	0.5025
f(x(i))/y(i)	2.1132	2.2222	2.3382	2.4623	2.5958	2.7406	2.8988	3.0733	3.2678	3.4873
h*(f(x))	0.01056	0.0111	0.0116	0.0123	0.0129	0.0137	0.0144	0.0153	0.0163	0.0174
Simpson usuli
	0.0525	0.1025	0.1525	0.2025	0.2525	0.3025	0.3525	0.4025	0.4525	0.5025
f(x(i))/y(i)	1.0539	1.1083	1.1661	1.2279	1.2944	1.3665	1.4452	1.532	1.6287	1.7378
h/3*(f(x))	0.00527	0.00554	0.00583	0.00614	0.00647	0.00683	0.00723	0.00766	0.00814	0.00868

3. Berilgan algebraik va transsendent tenglamalarni yechishda oraliqni teng ikkiga
bo‘lish va vatarlar usullaridan foydalanib tenglamaning taqribiy ildizini 0.1, 0.01, 0.001,
0.0001, 0.00001, 0.000001 aniqliklarda hisoblansin. Olingan natijalar quyidagi jadvalga
to’ldirilib tahlil qilinsin.

1) Ikkiga bo’lish usuli:


Algoritm

Boshlash


double a,b,c,e,x; int s=0a[


a,b,e ni kiriting



If(funksiya(a) *funksiya(b)<0)


Tamom

x ni chiqar

“Oraliq noto’g’ri” deb chiqar

x=c

While((b-a)/2>e

c=(a+b)/2
s=s+1

b=c

a=c

If(funksiya(a) *funksiya(c)<0)

c=(a+b)/2

#include

using namespace std;
double funksiya(double x){
return log(1+8/(1+x*x*x*x))-x*x+16;
}
int main(){
double a,b,c,e,x; int s=0;
cout<<"a="; cin>>a;
cout<<"b="; cin>>b;
cout<<"e="; cin>>e;
if(funksiya(a)*funksiya(b)<0){
c=(a+b)/2;
while((b-a)/2>e){
if(funksiya(a)*funksiya(c)<0)
b=c;
else
a=c;
c=(a+b)/2;
s+=1;
}
x=c;
cout<<"x="< cout< }
else
cout<<"oraliq noto'g'ri";
}

2) Vatarlar usuli:


Algoritm



#include
using namespace std;
double F(double x){
return log(1+8/(1+x*x*x*x))-x*x+16;
}
double F1(double x){
return log(1+8/(1+x*x*x*x))-x*x+16;
}
double F2(double x){
log(1+8/(1+x*x*x*x))-x*x+16;
}
int main(){
double a, b, S=0, x1, x2, e;
cout<<"a="; cin>>a;
cout<<"b="; cin>>b;
cout<<"e="; cin>>e;
if(F1(a)*F2(a)>0) x1=a;
else goto _2;
_1:
x2=x1-F(x1)*(b-x1)/(F(b)-F(x1));
if(F1(a)*F2(a)<0) x1=b;
if(abs(x2-x1)>e){
x1=x2;
goto _1;
}
else goto _3;
_2:
if(F1(a)*F2(a)<0) x1=b;
_4:
x2=x1-F(x1)*(x1-a)/(F(x1)-F(a));
if(abs(x1-x2)>e){
x1=x2;
goto _4;
}
_3:
cout< return 0;

}

Usul \ e=	0.1	0.01	0.001	0.0001	0.00001	0.000001
Kesmani teng 2 ga bo’lish	-1.30	-1.331254	-1.333597	-1.333310	-1.3332714	-1.3332717
Vatarlar usuli	-1.32843	-1.32843	-1.3331	-1.33327	-1.33327	-1.3332723