辛普森算法

double func(double a, double b, double x) {
  double r = a * exp(- x*x) + b * sqrt(x);
  return r*r;//return的积分常数，例如这里f（x*x）dx|[0,h]
}

double integrate(double a, double b, double h) {
  unsigned long steps = 1, it = 1;
  double V = h * (func(a, b, 0) + func(a, b, h)) / 2.0;
  double Vold;

  do {
    double tmp = 0;
    steps *= 2;
    //cout << V << endl;

    for (unsigned long i = 1; i < steps; i += 2) {
      tmp += func(a, b, (h * i) / steps);
    }

    Vold = V;
    V = (V / 2.0) + ((tmp * h) / steps);
  } while (fabs(V - Vold) > eps);

  return V;
}
/*上述模板：func（）为积分的函数，integrate（）为区间【0，h】上的积分*/