108-guruh talabasi Eshmo’minov Otabek. 2-mustaqil ish. Quyidagi nazariy savollarga javob bering

Program integral1(input,output);

Uses crt;

var a,b,h,s,J:real;

i,n:integer;

{nostandart funktsiyani tavsiflaymiz}

function f(x:real):real;

begin

f:=ln(x*x+3*x+1);

end;

begin clrscr;

write(‘quyi chegara a=’); readln(a);

write(‘yuqori chegara b=’); readln(b);

write(‘bo’laqlar soni n=’); readln(n);

s:=(f(a)+f(b))/2; h:=(b-a)/n;

for i:=2 to n do

s:=s+f(a+(i-1)*h);

J:=h*s; textcolor(13);

writeln(‘integral kiymati J=’,J:3:4);

end.

{Simpson usuli} Program integral2(input,output); Uses crt; var a,b,h,s,J:real; i,n,k:integer; function f(x:real):real; begin f:=ln(x*x+3*x+1); end; begin clrscr; write(‘quyi chegara a=’); readln(a); write(‘yuqori chegara b=’); readln(b); write(‘bo’laqlar soni n=’); readln(n); h:=(b-a)/n; s:=f(a)+f(b); k:=1; for i:=2 to n do begin s:=s+(3+k)*f(a+(i-1)*h); k=-k end; J:=s*h/3; textcolor(2); writeln(‘integral qiymati J=’,J:3:4); end.

2. 
   Quyidagi masalalar uchun algoritm tuzing va uni tahlil qiling. Dastur kodini yozib natija oling.
   

1-masala.

Savol : Ikki o’lchamli kvadrat matritsa berilgan. Uning har bir satridagi eng kata elementlarini aniqlash dasturini tuzing.

Dastur kodi :

#include

#include

using namespace std;

void matrix_print(int a[10][10], int m, int n)

{

// matritsani jadval shaklida chiqarish

for (int i = 0; i < m; i++)

{

for (int j = 0; j < n; j++)

{

cout << a[i][j] << "\t";

}

cout << "\n";

}

}

int satr_max(int a[], int n)

{

// massivning eng katta elementini aniqlash

int max = a[0];

for (int i = 1; i < n; i++)

if (max < a[i]) max = a[i];

return max;

}

int main()

{

int m, n, a[10][10];

cout << "Satrlar sonini kiriting \nm="; cin >> m;

cout << "Ustunlar sonini kiriting \nn="; cin >> n;

cout <<"Massiv elementlarini kiriting \n";

for (int i = 0; i < m; i++)

for (int j = 0; j < n; j++)

cin >> a[i][j];

cout << "Kiritilgan matritsa\n";

//funksiyaga matritsa, satrlar va ustunlar soni jo'natiladi

matrix_print(a, m, n);

for (int i = 0; i < m; i++)

{

// funksiyaga i-satrning 0-elementi adresini

// va elementlar sonini jo'natamiz

cout << i << "-satrning eng kattasi=" <<

satr_max(&a[i][0], n);

cout << endl;

}

return 0;

}



2-masala.

Quyidagi funksiyani to’rtburchaklar, Trapetsiya va Simpson formulalari yordamida taqribiy hisoblash dasturini tuzing



.

To’g’ri to’rtburchaklar formulasi. Bu formulani keltirib chiqarish uchun dastlab kesmani nuqtalar bilan n ta teng bo’lakka bo’lamiz.

Buning uchun integrallash kesmasini ta bo’lakka bo’lamiz va hisoblashlar natijalarini keltiramiz:

Bizning misolda bo’lgani uchun, to’g’ri to’rtburchaklar formulasiga asosan, quyidagi natijani hosil qilamiz.

X=0.1; =0.9901

X=0.2; =0.9615

X=0.3; =0.9174

X=0.4; =0.8621

….

X=1.0 =0.5000

7.5998

integralni trapetsiyalar formulasi yordamida taqribiy hisoblang. Bunda ham

deb oldik :

Yechish: va

bo’lgani uchun

Dastur kodi

#include

#include

using namespace std;

double funk(double x)

{

return (sin(x)) / (1+x*x));

}

int main()

{

double a,b,S=0, xa;

int n=10;

cout<<"integral chegarasini kiriting"<

cin>>a>>b;

xa=a+0.1;

while (xa

{

S+=funk(xa);

xa+=0.1;

}

S=(a+b)/2+S;

S=S*fabs(b-a)/n;

cout << S;

return 0;

}