自适应simpton积分模板
double f(double x){
return b*sqrt(1-(x*x)/(a*a));
}
double simpton(double a,double b){
double c=(a)+(b-a)/2;
return (f(a)+4*f(c)+f(b))*(b-a)/6;
}
double integral(double L,double R,double Eps){
double mid=L+(R-L)/2;
double ST=simpson(L,R),SL=simpson(L,mid),SR=simpson(mid,R);
if (fabs(SL+SR-ST)<=15*Eps) return SL+SR+(SL+SR-ST)/15;
return integral(L,mid,Eps/2)+integral(mid,R,Eps/2);
}
