Tp rule 

#include <stdio.h>

float f(float x) {
    return x * x;  // Example function f(x) = x^2
}

float trapezoidalRule(float a, float b, int n) {
    float h = (b - a) / n;
    float sum = f(a) + f(b);
    for (int i = 1; i < n; i++) {
        sum += 2 * f(a + i * h);
    }
    return (h / 2) * sum;
}

int main() {
    float a, b;
    int n;
    printf("Enter lower limit (a): ");
    scanf("%f", &a);
    printf("Enter upper limit (b): ");
    scanf("%f", &b);
    printf("Enter number of subintervals (n): ");
    scanf("%d", &n);
    printf("Result: %f\n", trapezoidalRule(a, b, n));
    return 0;
}

simpson 1/3
#include <stdio.h>

float f(float x) {
    return x * x;  // Example function f(x) = x^2
}

float simpsonsOneThirdRule(float a, float b, int n) {
    if (n % 2 != 0) {
        printf("Number of intervals must be even.\n");
        return -1;
    }
    float h = (b - a) / n;
    float sum = f(a) + f(b);
    for (int i = 1; i < n; i++) {
        if (i % 2 == 0) {
            sum += 2 * f(a + i * h);
        } else {
            sum += 4 * f(a + i * h);
        }
    }
    return (h / 3) * sum;
}

int main() {
    float a, b;
    int n;
    printf("Enter lower limit (a): ");
    scanf("%f", &a);
    printf("Enter upper limit (b): ");
    scanf("%f", &b);
    printf("Enter number of subintervals (n): ");
    scanf("%d", &n);
    float result = simpsonsOneThirdRule(a, b, n);
    if (result != -1) {
        printf("Result: %f\n", result);
    }
    return 0;
}

weddls Ruls
#include <stdio.h>

float f(float x) {
    return x * x;  // Example function f(x) = x^2
}

float weddlesRule(float a, float b) {
    float h = (b - a) / 6;
    return (3 * h / 10) * (f(a) + 5 * f(a + h) + f(a + 2 * h) + 6 * f(a + 3 * h) + f(a + 4 * h) + 5 * f(a + 5 * h) + f(b));
}

int main() {
    float a, b;
    printf("Enter lower limit (a): ");
    scanf("%f", &a);
    printf("Enter upper limit (b): ");
    scanf("%f", &b);
    printf("Result: %f\n", weddlesRule(a, b));
    return 0;
}

booles rule 
#include <stdio.h>

float f(float x) {
    return x * x;  // Example function f(x) = x^2
}

float boolesRule(float a, float b) {
    float h = (b - a) / 4;
    return (2 * h / 45) * (7 * f(a) + 32 * f(a + h) + 12 * f(a + 2 * h) + 32 * f(a + 3 * h) + 7 * f(b));
}

int main() {
    float a, b;
    printf("Enter lower limit (a): ");
    scanf("%f", &a);
    printf("Enter upper limit (b): ");
    scanf("%f", &b);
    printf("Result: %f\n", boolesRule(a, b));
    return 0;
}

bisectoin method 
#include <stdio.h>
#include <math.h>

float f(float x) {
    return x * x - 4;  // Example function f(x) = x^2 - 4
}

void bisectionMethod(float a, float b, float tol) {
    if (f(a) * f(b) >= 0) {
        printf("Invalid interval. f(a) and f(b) must have opposite signs.\n");
        return;
    }
    float c;
    while ((b - a) >= tol) {
        c = (a + b) / 2;
        if (f(c) == 0.0) {
            break;
        } else if (f(c) * f(a) < 0) {
            b = c;
        } else {
            a = c;
        }
    }
    printf("Root: %f\n", c);
}

int main() {
    float a, b, tol;
    printf("Enter interval [a, b]: ");
    scanf("%f %f", &a, &b);
    printf("Enter tolerance: ");
    scanf("%f", &tol);
    bisectionMethod(a, b, tol);
    return 0;
}

newton rep
#include <stdio.h>
#include <math.h>

float f(float x) {
    return x * x - 4;  // Example function f(x) = x^2 - 4
}

float f_derivative(float x) {
    return 2 * x;  // Derivative of f(x)
}

void newtonRaphsonMethod(float x0, float tol) {
    float x1;
    while (1) {
        x1 = x0 - f(x0) / f_derivative(x0);
        if (fabs(x1 - x0) < tol) {
            printf("Root: %f\n", x1);
            return;
        }
        x0 = x1;
    }
}

int main() {
    float x0, tol;
    printf("Enter initial guess: ");
    scanf("%f", &x0);
    printf("Enter tolerance: ");
    scanf("%f", &tol);
    newtonRaphsonMethod(x0, tol);
    return 0;
}

g elements method 

#include <stdio.h>

void gaussElimination(float a[10][10], int n) {
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            float ratio = a[j][i] / a[i][i];
            for (int k = 0; k <= n; k++) {
                a[j][k] -= ratio * a[i][k];
            }
        }
    }
    float x[10];
    for (int i = n - 1; i >= 0; i--) {
        x[i] = a[i][n];
        for (int j = i + 1; j < n; j++) {
            x[i] -= a[i][j] * x[j];
        }
        x[i] /= a[i][i];
    }
    printf("Solution:\n");
    for (int i = 0; i < n; i++) {
        printf("x[%d] = %f\n", i, x[i]);
    }
}

int main() {
    int n;
    float a[10][10];
    printf("Enter the number of equations: ");
    scanf("%d", &n);
    printf("Enter the augmented matrix:\n");
    for (int i = 0; i < n; i++) {
        for (int j = 0; j <= n; j++) {
            scanf("%f", &a[i][j]);
        }
    }
    gaussElimination(a, n);
    return 0;
}

regular falsi meetod
#include <stdio.h>
#include <math.h>

float f(float x) {
    return x * x - 4;  // Example function f(x) = x^2 - 4
}

void regulaFalsiMethod(float a, float b, float tol) {
    if (f(a) * f(b) >= 0) {
        printf("Invalid interval. f(a) and f(b) must have opposite signs.\n");
        return;
    }
    float c;
    while (fabs(b - a) >= tol) {
        c = (a * f(b) - b * f(a)) / (f(b) - f(a));
        if (f(c) == 0.0) {
            break;
        } else if (f(c) * f(a) < 0) {
            b = c;
        } else {
            a = c;
        }
    }
    printf("Root: %f\n", c);
}

int main() {
    float a, b, tol;
    printf("Enter interval [a, b]: ");
    scanf("%f %f", &a, &b);
    printf("Enter tolerance: ");
    scanf("%f", &tol);
    regulaFalsiMethod(a, b, tol);
    return 0;
}