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 <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define N 3
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<n; 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<n; 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<n; 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<z; i++)
{
Tn = Tn+fun(x+i*h);
}
Tn = Tn*h;
return Tn;
}