Berilgan integral qiymatini to‘g‘ri to‘rtburchaklar, trapetsiyalar, Simpson usullarida ε>0 aniqlikda hisoblang. Aniqlikka erishganlik sharti sifatida

Aburasulov Alijonning Algoritmlarni loyihalash fanidan 1-amaliy ishi.

3. 
   variant.
   

Berilgan integral qiymatini to‘g‘ri to‘rtburchaklar, trapetsiyalar, Simpson usullarida ε>0 aniqlikda hisoblang. Aniqlikka erishganlik sharti sifatida |S2n-Sn|<ε tengsizlikdan foydalaning (boshlang‘ich n=10 deb olish mumkin). Natijaga erishish uchun zarur bo‘lgan qadamlar soni va integral taqribiy qiymati chiqariladi. С++ dasturida natijani oling.
(x²+3x+1)*tg(x-0,5) [0,5;1,5]

1. 
   to`g`ri to`rtburchak usuli:
   

#include
#include
using namespace std;
int main(){
int n=10,k=0;
float a=0.5,b=1.5,e,x,h,s0=1000000,s1=0;
cout<<"Integral 'To`g`ri to`rtburchak' usulida hisoblanadi "<
cout<<"Qanday aniqlikda hisoblansin : ";
cin>>e;


while(1){
h=(b-a)/n;
for(int i=0;i<=n;i++){
x=a+i*h;
s1+=(x*x+3*x+1) * tan(x-0.5);
}
s1*=h;
if(fabs(s1-s0)
{
cout<<" Natija : "<
cout<<" Qadamlar soni : "<
break;
}
else {
s0=s1;
s1=0;
k++;
n*=2;
}
} }

2. 
   trapetsiya usuli:
   

#include
#include
using namespace std;
int main(){
int n=10,k=0;
float a=0.5,b=1.5,e,x,h,s0=1000000,s1=0;
cout<<"Integral 'Trapetsiya' usulida hisoblanadi "<
cout<<"Qanday aniqlikda hisoblansin : ";
cin>>e;
while(1){
h=(b-a)/n;
for(int i=0 ; i<=n ; i++){
x=a+i*h;
if(i==0 or i==n) s1+=(x*x+3*x+1) * tan(x-0.5);
else s1+=2*(x*x+3*x+1) * tan(x-0.5);
}
s1*=h/2;
if(fabs(s1-s0)
cout<<"Natija : "<
cout<<" \n Qadamlar soni : "<
break;
}
else {
s0=s1;
s1=0;
n*=2;
k++;
}
}
}

3. 
   Simpson usuli:
   

#include
#include
using namespace std;
int main(){
int n=10,k=0;
float a=0.5,b=1.5,e,x,h,s0=1000000,s1=0;
cout<<"Integral 'Simpson' usulida hisoblanadi "<
cout<<"Qanday aniqlikda hisoblansin : ";
cin>>e;
while(1){
h=(b-a)/n;
for(int i=0 ; i<=n ; i++){
x=a+i*h;
if(i==0 or i==n) s1+=(x*x+3*x+1) * tan(x-0.5);
else if (i%2==0) s1+=4*(x*x+3*x+1) * tan(x-0.5);
else s1+=2*(x*x+3*x+1) * tan(x-0.5);
}
s1*=h/3;
if(fabs(s1-s0)
{
cout<<"Natija : "<
cout<<" Qadamlar soni : "<
break;
}
else {
s0=s1;
s1=0;
n*=2;
k++;
}
}
}