求定积分的方法有很多种，下面是我总结的几种比较常用的方法。
#include
#include
#include
#include
#define N3
double fun(double x)
{
double y;
y = sqrt(4-(x)*(x));
//y = sin(x);
return y;
}
/*随机点法求定积分*/
double Darts(int n)
{
double x, y;
time_t t;
int i = 0;
int count = 0;
srand((unsigned)time(&t));
for (i=0; i
{
x = rand()%100/100.0;
y = rand()%100/100.0;
if (y <= 1-pow(x,2))
{
count++;
}
}
return (double)count/(double)n;
}
/*左矩形法求定积分*/
double LeftRect(double down, double up, int n)
{
double h, s;
int i;
/*计算步长*/
h = (up-down)/n;
s = fun(down)*h;
for (i=1; i
{
s = s + fun(down+i*h)*h;
}
return s;
}
/*梯形公式求定积分*/
double Trape(double down, double up, int n)
{
double h, s;
int i = 0;
/*计算步长*/
h = (up-down)/n;
s = 0.5*(fun(down)+fun(down+h))*h;
for (i=1; i
{
s = s + 0.5 * (fun(down+i*h) + fun(down+(i+1)*h))*h;
}
return s;
}
/*复合梯形公式*/
double T(double x, double y, int z)
{
double h, Tn;
int i = 0;
h = (y-x)/z;
Tn = (fun(x)+fun(y))/2;
for (i=0; i
{
Tn = Tn+fun(x+i*h);
}
Tn = Tn*h;
return Tn;
}
/*辛普生公式求定积分，公式为：S[n]=(4*T[2*n]-T[n])/3，其中T[2n],T[n]为梯形公式计算结果*/
double Simposn(double down, double up, int n)
{
double s;
/*辛普生公式*/
s = (4*T(down, up, 2*n) - T(down, up, n))/3;
return s;
}
/*高斯公式求定积分*/
double Gass(double (*func)(double x), double a, double b, int n)
{
int i = 0;
//高斯点及其求积系数列表
float x1[1]={0.0};
float A1[1]={2};
float x2[2]={-0.5573503,0.5573503};
float A2[2]={1,1};
float x3[3]={-0.7745967,0.0,0.7745967};
float A3[3]={0.555556,0.888889,0.555556};
float x4[4]={0.3399810,-0.3399810,0.8611363,-0.8611363};
float A4[4]={0.6521452,0.6521452,0.3478548,0.3478548};
float x5[5]={0.0,0.5384693,-0.5384693,0.9061799,-0.9061799};
float A5[5]={0.5688889,0.4786287,0.4786287,0.2369269,0.2369269};
float *p, *t;
switch (n)
{
case 1:
p = x1;
t = A1;
break;
case 2:
p = x2;
t = A2;
break;
case 3:
p = x3;
t = A3;
break;
case 4:
p = x4;
t = A4;
break;
case 5:
p = x5;
t = A5;
break;
default :
printf("intput wrong!");
}
float g = 0;
for (i=0; i
{
g += (*func)((b-a)*p[i]/2+(a+b)/2)*t[i];
}
g *= (b-a)/2;
return g;
}
int main(int argc, char *argv[])
{
printf("随机点法积分值%f\n", Darts(10000));
double down, up;
int n;
double sum = 0;
printf("积分下限:\n");
scanf("%lf", &down);
printf("积分上限:\n");
scanf("%lf", &up);
printf("分隔数目:\n");
scanf("%d", &n);
sum = LeftRect(down, up, n);
printf("左矩形法积分值为:%f\n", sum);
sum = Trape(down, up, n);
printf("梯形公式积分值为:%f\n", sum);
sum = Simposn(down, up, n);
printf("辛普生公式积分值为:%f\n", sum);
sum = Gass(fun, down, up, N);
printf("高斯公式积分值为:%f\n", sum);
return 0;
}
