117.求定积分

  

   

    

     

    
    

     

      #include "stdio.h"
     
    
   

    

     

    
    

     

      #include "math.h"
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      double fsimpf(x) /*要进行计算的被积函数*/
     
    
   

    

     

    
    

     

      double x;
     
    
   

    

     

    
    

     

      {
     
    
   

    

     

    
    

     
	double y;
     
    
   

    

     

    
    

     

          y=log(1.0+x)/(1.0+x*x);
     
    
   

    

     

    
    

     
    return(y);
     
    
   

    

     

    
    

     

      }
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      double fsimp(a,b,eps) /*辛普森算法*/
     
    
   

    

     

    
    

     

      double a,b,eps; /*a为积分下限，b为积分上限，eps是希望达到的精度*/
     
    
   

    

     

    
    

     

      {
     
    
   

    

     

    
    

     
    int n,k;
     
    
   

    

     

    
    

     
    double h,t1,t2,s1,s2,ep,p,x;
     
    
   

    

     

    
    

     

          n=1; h=b-a;
     
    
   

    

     

    
    

     

          t1=h*(fsimpf(a)+fsimpf(b))/2.0;  /*用梯形公式求出一个大概的估值*/
     
    
   

    

     

    
    

     

          s1=t1;
     
    
   

    

     

    
    

     

          ep=eps+1.0;
     
    
   

    

     

    
    

     
    while (ep>=eps)
     
    
   

    

     

    
    

     

      	{
     
    
   

    

     

    
    

     
		/*用梯形法则计算*/
     
    
   

    

     

    
    

     

      		p=0.0;
     
    
   

    

     

    
    

     
		for (k=0;k<=n-1;k++)
     
    
   

    

     

    
    

     

      		{
     
    
   

    

     

    
    

     

      			x=a+(k+0.5)*h;
     
    
   

    

     

    
    

     

      			p=p+fsimpf(x);
     
    
   

    

     

    
    

     

      		}
     
    
   

    

     

    
    

     

      		t2=(t1+h*p)/2.0;
     
    
   

    

     

    
    

     
		/*用辛普森公式求精*/
     
    
   

    

     

    
    

     

      		s2=(4.0*t2-t1)/3.0;
     
    
   

    

     

    
    

     

      		ep=fabs(s2-s1);
     
    
   

    

     

    
    

     

      		t1=t2; s1=s2; n=n+n; h=h/2.0;
     
    
   

    

     

    
    

     

      	}
     
    
   

    

     

    
    

     
    return(s2);
     
    
   

    

     

    
    

     

      }
     
    
   

    

     

    
    

     

      main()
     
    
   

    

     

    
    

     

      {
     
    
   

    

     

    
    

     
	double a,b,eps,t;
     
    
   

    

     

    
    

     

              a=0.0; b=1.0; eps=0.0000001;
     
    
   

    

     

    
    

     
    	clrscr();
     
    
   

    

     

    
    

     
	puts("**********************************************************");
     
    
   

    

     

    
    

     
	puts("* This program is to calculat the Value of *");
     
    
   

    

     

    
    

     
	puts("* a definite integral by Simpson Method. *");
     
    
   

    

     

    
    

     
	puts("**********************************************************");
     
    
   

    

     

    
    

     

          	t=fsimp(a,b,eps);
     
    
   

    

     

    
    

     
	puts("\n----------------------------------------------------------");
     
    
   

    

     

    
    

     
	printf(" >> The result of definite integral is : \n");
     
    
   

    

     

    
    

     
	printf(" >> SIGMA(0,1)ln(1+x)/(1+x^2)dx = ");
     
    
   

    

     

    
    

     
    	printf("%e\n",t);
     
    
   

    

     

    
    

     
    	puts("----------------------------------------------------------");
     
    
   

    

     

    
    

     
    	printf("\n Press any key to quit...");
     
    
   

    

     

    
    

     
	getch();
     
    
   

    

     

    
    

     

      }
     
    
  
 

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原文链接：blog.csdn.net/weixin_41055260/article/details/124576484