#include <stdio.h>
#include <math.h>
#define F(X) (4.0/(1+X*X))
static float EPS = 1.0E-14
static int COUNT=1
static double a=0.0, b=1.0
static double M[32],T[32],S[32],C[32],R[32],E[32]
double GETM(int K)
{ unsigned long j,n=1
double x=0,y=0,step=0
for(j=0j<Kj++) n*=2
step = (b-a)/n
x = a+step/2
for(j=0j<nj++){y+=F(x)x+=step}
return (y*step)
}
Simpson(float EPS)
{ int k=0
T[0]= (b-a)*(F(a)+F(b))/2.0
S[0]=T[0]
E[0]=1.0E10
for(k=0k<20k++)
{ M[k] = GETM(k)
T[k+1]=(M[k]+T[k])/2.0
S[k+1]=(4.0*T[k+1]-T[k])/3.0
COUNT++
E[k+1]=fabs(S[k+1]-S[k])
if(k<3)continue
if(E[k+1]<EPS)break
}
return
}
ShawResult()
{ int k
system("cls"弊顷让)
printf("\n K M[K] T[K] S[K]")
printf(" E[K]")
printf("\n-------------------------------------------")
printf("-----------------------------------")
for(k=0k<COUNTk++)
printf("\n%2d %20.15lf%20.15lf%20.15lf%12.4e",k,M[k],T[k],S[k],E[k])
printf("\n--------------------------------------------")
printf("-----------------------------------")
getch()
system("cls")
return
}
SaveResult()
{ int k
FILE * fp
fp=fopen("Simpson.htm","w")
if(!fp) return
fprintf(fp,"租局<html><head></head>乎含")
fprintf(fp,"<body bgcolor = #006699 text = #FFff00>")
fprintf(fp,"<pre><font size=\"6\">")
fprintf(fp,"\n K M[K] T[K] S[K]")
fprintf(fp," E[K]")
fprintf(fp,"\n----------------------------------------------")
fprintf(fp,"----------------------------------")
for(k=0k<COUNTk++)
fprintf(fp,"\n%2d %20.15f%20.15f%20.15f%12.4le",k,M[k],T[k],S[k],E[k])
fprintf(fp,"\n----------------------------------------------")
fprintf(fp,"----------------------------------")
fprintf(fp,"</pre></font></body>")
fclose(fp)
return
}
main()
{ Simpson(EPS)
ShawResult()
SaveResult()
}
用MATLAB程序计算微积分问题：
>>%总练习题1——（2）
>>syms x
>>limit((1+3/x)^x,x,inf)
ans =exp(3)
>>%总练习题1——（3）
>>syms f(x) g(x)
>>f(x)=x^2+1g(x)=1/(x+1)
>>f(g(2))
ans =10/9
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