n – Number of parts
h = (xn - x0) / n
x[i] = x0 + i * h
ytimestwo = Summation ( y[i] * 2 )
answer = ( h/2.0 ) * ( y[0] + y[n] + ytimestwo );
#include<stdio.h>
#include<math.h>
#include<conio.h>
float f(float x){
return log(x);
};
int main(){
float x0, xn, h, y[20], x[20], ytimestwo, ans;
int i, n;
clrscr();
printf("Enter the value of x0, xn, and n. (Maximum value of n is 21.)\n");
scanf("%f %f %d", &x0, &xn, &n);
h = (xn-x0)/n;
ytimestwo = 0.0;
for(i=1; i<=n; i++){
x[i] = x0 + i * h;
y[i] = f(x[i]);
printf("x: %8.5f, y: %8.5f\n", x[i], y[i]);
ytimestwo = ytimestwo + 2*y[i];
}
ans = (h/2.0) * (y[0] + y[n] + ytimestwo);
printf("\nThe value of integration is %f",ans);
getch();
}n – Number of parts
h = (xn - x0) / n
x[i] = x0 + i * h
se = Summation ( 2 * y[i] ) where i is even
so = Summation ( 4 * y[i] ) where i is odd
answer = ( h / 3.0 ) * ( y[0] + y[n] + se + so );
#include <stdio.h>
#include <math.h>
void main()
{
float func(float);
float h, se, so, ans;
se = 0.0;
so = 0.0;
int i, n;
float x[20], y[20];
printf("\nEnter number of parts(Max 20): ");
scanf("%d", &n);
printf("\nEnter the upper and lower limts.\n");
scanf("%f %f", &x[0], &x[n]);
y[0] = func(x[0]);
h = (x[n] - x[0]) / n;
for (i = 1; i < n; i++)
{
x[i] = x[0] + i * h;
y[i] = func(x[i]);
printf("\nx: %8.5f, y: %8.5f\n", x[i], y[i]);
if (i % 2 == 0)
{
se += 2 * y[i];
}
else
{
so += 4 * y[i];
}
}
y[n] = func(x[n]);
ans = (h / 3.0) * (y[0] + y[n] + se + so);
printf("\nThe answer is: %f\n", ans);
}
float func(float x)
{
float g;
g = sin(x) - log(x) + exp(x);
return g;
}n – Number of parts
h = (xn - x0) / n
x[i] = x0 + i * h
mul_3 = Summation ( 2 * y[i] ) where i is a multiple of 3
not_mul_3 = Summation ( 3 * y[i] ) where i is not a multiple of 3
answer = ( ( 3 * h ) / 8.0 ) * ( y[0] + y[n] + mul3 + not_mul_3 );
#include <stdio.h>
#include <math.h>
void main()
{
float func(float);
float h, mul_3, not_mul_3 , ans;
mul3 = 0.0;
not_mul_3 = 0.0;
int i, n;
float x[20], y[20];
printf("\nEnter number of parts: ");
scanf("%d", &n);
printf("\nEnter the upper and lower limts.\n");
scanf("%f %f", &x[0], &x[n]);
y[0] = func(x[0]);
h = (x[n] - x[0]) / n;
for (i = 1; i < n; i++)
{
x[i] = x[0] + i * h;
y[i] = func(x[i]);
printf("\nx: %8.5f, y: %8.5f\n", x[i], y[i]);
if (i % 3 == 0)
{
mul3 += 2 * y[i];
}
else
{
not_mul_3 += 3 * y[i];
}
}
y[n] = func(x[n]);
ans = ((3*h) / 8.0) * (y[0] + y[n] + mul3 + not_mul_3);
printf("\nThe answer is: %f\n", ans);
}
float func(float x)
{
float g;
g = sin(x) - log(x) + exp(x);
return g;
}n – Number of parts
h = (xn - x0) / n
x[i] = x0 + i * h
k1 = Summation ( 2 * y[i] ) where i is a multiple of 6
k2 = Summation ( 6 * y[i] )where i is a multiple of 3
k3 = Summation ( y[i] ) where i is a multiple of 2
k4 = Summation ( 5 * y[i] ) all the rest of the terms
answer = ( ( 3 * h ) / 10.0 ) * (y[0] + y[n] + k1 + k2 + k3 + k4);
#include <stdio.h>
#include <math.h>
void main()
{
float func(float);
float h, k1, k2, k3, k4, ans;
k1 = 0;
k2 = 0;
k3 = 0;
k4 = 0;
int i, n;
float x[20], y[20];
printf("\nEnter number of parts: ");
scanf("%d", &n);
printf("\nEnter the upper and lower limts.\n");
scanf("%f %f", &x[0], &x[n]);
y[0] = func(x[0]);
h = (x[n] - x[0]) / n;
for (i = 1; i < n; i++)
{
x[i] = x[0] + i * h;
y[i] = func(x[i]);
printf("\nx: %8.5f, y: %8.5f\n", x[i], y[i]);
if (i % 6 == 0)
{
k1 += 2 * y[i];
}
else if (i % 3 == 0)
{
k2 += 6 * y[i];
}
else if (i % 2 == 0)
{
k3 += y[i];
}
else
{
k4 += 5 * y[i];
}
}
y[n] = func(x[n]);
ans = ((3 * h) / 10.0) * (y[0] + y[n] + k1 + k2 + k3 + k4);
printf("\nThen answer is: %f\n", ans);
}
float func(float x)
{
float g;
g = sin(x) - log(x) + exp(x);
return g;
} n – Number of parts
h = (xn - x0) / n
x[i] = x0 + i * h
k1 = Summation ( 14 * y[i] ) where i is a multiple of 4
k2 = Summation ( 12 * y[i] )where i is a multiple of 2
k3 = Summation ( y[i] ) where i is a multiple of 2
answer = ( (2 * h) / (45.0) ) * ( y[0] + y[n] + k1 + k2 + k3 );
#include <stdio.h>
#include <math.h>
void main()
{
float func(float);
float h, k1, k2, k3, ans;
k1 = 0;
k2 = 0;
k3 = 0;
int i, n;
float x[20], y[20];
printf("\nEnter number of parts: ");
scanf("%d", &n);
printf("\nEnter the upper and lower limts.\n");
scanf("%f %f", &x[0], &x[n]);
y[0] = 7 * func(x[0]);
h = (x[n] - x[0]) / n;
for (i = 1; i < n; i++)
{
x[i] = x[0] + i * h;
y[i] = func(x[i]);
printf("\nx: %8.5f, y: %8.5f\n", x[i], y[i]);
if (i % 4 == 0)
{
k1 += 14 * y[i];
}
else if (i % 2 == 0)
{
k2 += 12 * y[i];
}
else
{
k3 += 32*y[i];
}
}
y[n] = 7*func(x[n]);
ans = ((2 * h) / (45.0)) * (y[0] + y[n] + k1 + k2 + k3 + k4);
printf("\nThen answer is: %f\n", ans);
}
float func(float x)
{
float g;
g = sin(x) - log(x) + exp(x);
return g;
}x0 – initial value of x
y0 – initial value of y at x0
h – width of the strip
Initialize x and y
x = x0
y = y0
[Begin Loop] (Run Until we reach xn)
k1 = h * function( x, y )
k2 = h * function( x + h/2 , y + k1 / 2.0)
k3 = h * function( x + h/2 , y + k2 / 2.0)
k4 = h * function( x + h/2 , y + k3 * h)
answer = y0 + ((1.0 / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4));
Increment x and y
x = x + h;
y = y + k * h;
[Loop]
#include <stdio.h>
float f(float x, float y);
int main()
{
float x0, y0, k1, k2, k3, k4, k, y, x, h, xn;
printf("Enter x0, y0, xn, h:");
scanf("%f %f %f %f", &x0, &y0, &xn, &h);
x = x0;
y = y0;
printf("\n \n X \t \t Y\n");
while (x < xn)
{
k1 = f(x, y);
k2 = f((x + h / 2.0), (y + k1 / 2.0));
k3 = f((x + h / 2.0), (y + k2 / 2.0));
k4 = f((x + h), (y + k3 * h));
k = ((k1 + 2 * k2 + 2 * k3 + k4) / 6);
y += k*h;
x += h;
printf("%f \t %f \n", x, y);
}
}
float f(float x, float y)
{
float m;
m = 2 * x;
return m;
}#include <stdio.h>
#include <math.h>
float func(float x, float y)
{
return 1;
}
void main()
{
int i, j;
float h, k, x, y, a, b, c, d, xy[200][200], ax[200], ans;
printf("Integral a to b, integral c to d (function) dx/dy");
printf("\n Enter the following values \n");
printf("\n a = ");
scanf("%f", &a);
printf("\n b = ");
scanf("%f", &b);
printf("\n c = ");
scanf("%f", &c);
printf("\n d = ");
scanf("%f", &d);
printf("\n h = ");
scanf("%f", &h);
printf("\n k = ");
scanf("%f", &k);
x = ((b - a) / h);
y = ((d - c) / k);
printf("\n x=%f , y=%f \n", x, y);
for (i = 0; i <= x; i++)
{
for (j = 0; j <= y; j++)
{
xy[i][j] = func(a + i * h, c + j * k);
}
}
for (i = 0; i <= x; i++)
{
ax[i] = 0;
for (j = 0; j <= y; j++)
{
if (j == 0 || j == y)
ax[i] += xy[i][j];
else if (j % 2 == 0)
ax[i] += 2 * xy[i][j];
else
ax[i] += 4 * xy[i][j];
}
ax[i] = (h / 3) * ax[i];
}
ans = 0;
for (i = 0; i <= x; i++)
{
if (i == 0 || i == x)
ans += ax[i];
else if (i % 2 == 1)
ans += 4 * ax[i];
else
ans += 2 * ax[i];
}
ans = (k / 3) * ans;
printf("\nValue of integral is %f", ans);
}