2-Topshiriq n = 10 uchun chap va o'ng to'rtburchaklar formulalari yordamida integralni hisoblang, olingan natijalarni taqqoslash orqali aniqlikni baholash

O‘ZBEKISTON RESPUBLIKASI AXBOROT TEXNOLOGIYALARI VA
KOMMUNIKATSIYALARINI RIVOJLANTIRISH VAZIRLIGI
MUHAMMAD AL-XORAZMIY NOMIDAGI
TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI
Kompyuter injiniring fakulteti



Algoritmlarni loyihalash fanidan


Amaliy ishi
Guruh: 241-21
Bajardi: To’ychiev Javohir
Tekshirdi: Nasriddinov Saloxiddin

Toshkent 2023

1. Matritsalar ustida amallarni bajaring.

#include

#include
#include
using namespace std;
vector calculateExpression(vector& A, vector& B) {
vector result;
int n = A.size();
for (int i = 0; i < n; i++) {
int a = A[i];
int b = B[i];
int temp = a*(2*a+b)-b*(a-b);
result.push_back(temp);
}
return result;
}
int main() {
vector A = {2,3,1,4,-1,0,0,1,2};
vector B = {9,8,7,2,7,3,4,3,5};
vector result = calculateExpression(A, B);
cout << "Natija: ";
for (int i = 0; i < result.size(); i++) {
cout << result[i] << " ";
}
cout << endl;
return 0;
}

2-Topshiriq . n = 10 uchun chap va o'ng to'rtburchaklar formulalari yordamida integralni hisoblang, olingan natijalarni taqqoslash orqali aniqlikni baholash.

#include

#include

using namespace std;

double f(double x) {

return sqrt(1.5*x+2.3)/3+sqrt(0.3*x+1);
}

int main() {

int n = 10;
double a = 0.8;
double b = 2.4;
double h = (b - a) / n;

double sumLeft = 0.0;

for (int i = 0; i < n; i++) {
double xi = a + i * h;
sumLeft += f(xi) * h;
}

double sumRight = 0.0;

for (int i = 1; i <= n; i++) {
double xi = a + i * h;
sumRight += f(xi) * h;
}

cout << "Chap tortburchak : " << sumLeft << endl;

cout << "O'ng tortburchak: " << sumRight << endl;

return 0;

}
3-Topshiriq Trapetsiya formulasi yordamida integralni hisoblang(E=0.001). 2. n=8 uchun Simpson formulasi yordamida integralni hisoblang; jadvalini tuzish orqali natijaning xatosini baholang

#include

#include
using namespace std;

double f(double x) {

return 1/sqrt(x*x+2.5);
}

int main() {

double a = 1.6;
double b = 2.2;
double E = 0.001;
double I = 0.0;
double I_old = 0.0;
int n = 1;
double h = (b-a)/n;

do {
I_old = I;

I = (f(a) + f(b))/2.0;
for (int i = 1; i < n; i++) {
double x = a + i*h;
I += f(x);
}
I *= h;
n *= 2;
h = (b-a)/n;
} while (abs(I - I_old) >= E);

cout << "Integralning yaqinlashishi: " << I << endl;

cout << "Subintervallar soni: " << n << endl;

return 0;

}
#include
#include
using namespace std;

double f(double x) {

return (x*x+1)*sin(x-0.5);
}

int main() {

double a = 0.8;
double b = 1.6;
int n = 8;
double h = (b-a)/n;
double sum_odd = 0.0;
double sum_even = 0.0;

for (int i = 1; i < n; i += 2) {

double x = a + i*h;
sum_odd += f(x);
}
for (int i = 2; i < n; i += 2) {
double x = a + i*h;
sum_even += f(x);
}

double I = (h/3.0)*(f(a) + 4.0*sum_odd + 2.0*sum_even + f(b));

double error = abs(I - 0.462985);
cout << "Integralning yaqinlashishi: " << I << endl;
cout << "Absolute xatoligi: " << error << endl;

return 0;

}

4-Topshiriq kesmani ikkiga bo`lish usuli
#include
#include
using namespace std;

double f(double x) {

return exp(-3*x);
}

double enumerate(double x0, double x1, double eps) {

double x = x0;
while (x <= x1) {
if (abs(f(x)) <= eps) {
return x;
}
x += eps;
}
return NAN;
}

double chords(double x0, double x1, double eps) {

double x = x1;
double x_prev = x0;
while (abs(x - x_prev) > eps) {
x_prev = x;
x -= f(x)*(x - x0)/(f(x) - f(x0));
}
return x;
}

int main() {

double x0 = 0.0;
double x1 = 1.0;
double eps = 0.0001;

double root_enum = enumerate(0, 1, eps);

if (!isnan(root_enum)) {
cout << "Koren naydenniy pereborom: " << root_enum << endl;
} else {
cout << "Koren ne nayden pereborom" << endl;
}

double root_chords = chords(x0, x1, eps);

cout << "Konen naydenniy xordoy: " << root_chords << endl;

return 0;

}

5-Topshiriq Ch.P.M. grafik va simpleks usulida yeching






Simpleks







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