1 #include<stdio.h>
2 #include<math.h>
3 #define maxlen 100
4 #define eps 0.5*1e-5
5 double a=0;
6 double b=1;
7 double f(double x){
8 return 4/(1+x*x);
9 }
10 double t(int n){
11 int i;
12 double sum, h = (b - a) / n;
13 for (i = 1; i < n; i++)
14 sum += f(a + i * h);
15 sum += (f(a) + f(b)) / 2;
16 return (h * sum);
17 }
18 int main()
19 {
20 printf("k\t T[k]\t\t S[k]\t\t C[k]\t\t R[k]\n");
21 double T[maxlen];
22 double S[maxlen];
23 double C[maxlen];
24 double R[maxlen];
25 int k=-1;
26 while(1){
27 k++;
28 int z=pow(2,k);
29 T[k]=t(z);
30 if(k>0){
31 S[k]=T[k]*4/3-T[k-1]/3;
32 }
33 if(k>1){
34 C[k]=S[k]*16/15-S[k-1]/15;
35 }
36 if(k>2){
37 R[k]=C[k]*64/63-C[k-1]/63;
38 }
39 printf("%d\t %lf\t %lf\t %lf\t %lf\n",k+1,T[k],S[k],C[k],R[k]);
40 if(k>3){
41 if (abs(R[k]-R[k-1])<eps){
42 break;
43 }
44 }
45 }
46 printf("a:0,b:1 f(x):4/(1+x*x) eps:0.5*1e-5 the result:%lf\n",R[k]);
47 return 0;
48 }
