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        3double 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;
} /*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<n; 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;
}