習題EX4-9-2 C++語言

習題EX4-9-2  C++語言

// C++ program to implement Trapezoidal rule
#include<stdio.h>
#include<math.h>

// A sample function whose definite integral's
// approximate value is computed using Trapezoidal
// rule
float y(float x)
{
  // Declaring the function f(x) = x( e^x-1)
    return ( x* (exp(x) -1) );
}

// Function to evalute the value of integral
float trapezoidal(float a, float b, float n)
{
 // Grid spacing
 float h = (b-a)/n;

 // Computing sum of first and last terms
 // in above formula
 float s = y(a)+y(b);

 // Adding middle terms in above formula
 for (int i = 1; i < n; i++)
  s += 2*y(a+i*h);

 // h/2 indicates (b-a)/2n. Multiplying h/2
 // with s.
 return (h/2)*s;
}

// Driver program to test above function
int main()
{
 // Range of definite integral
 float x0 = 0;
 float xn = 1;

 // Number of grids. Higher value means
 // more accuracy
 int n = 10;

 printf("Value of integral is %6.4f\n",
    trapezoidal(x0, xn, n));
 return 0;
}

設定 

 int n = 10;
結果
Value of integral is 0.5037

設定 

 int n = 100;
結果
Value of integral is 0.5000