【辛普森积分】初中平面几何 校OJ2441 ∫baf(x)dx≈(b−a)/6*[f(a)+4f((a+b)/2)+f(b)]

∫baf(x)dx≈b−a6[f(a)+4f(a+b2)+f(b)]

∫abf(x)dx≈b−a6[f(a)+4f(a+b2)+f(b)]

辛普森积分 ↑ 。

∫baf(x)dx≈b−a6[f(a)+4f(a+b2)+f(b)]

#include <bits/stdc++.h>
using namespace std;
const double efs = 1e-4;

double r;

double f (double x)
{
	double res = sqrt (r * r - x * x);
	return res;
}

double simpson (double a, double b)
{
	double t = (a + b) / 2;
	double res = (b - a) / 6 * (f (a) + 4 * f (t) + f (b) );
	return res;
}

double cmp (double a, double b)
{
	double t = (a + b) / 2;
	double s0 = simpson (a, b);
	double s1 = simpson (a, t);
	double s2 = simpson (t, b);
	if (abs (s1 + s2 - s0) <= efs)  //满足精度条件
		return s0;
	else  //递归
		return cmp (a, t) + cmp (t, b);
		//两边分别求值
}

int main()
{
	double a, b;
	scanf ("%lf%lf%lf", &r, &a, &b);
	printf ("%.2f\n", cmp (a, f (b) ) - (f (b) - a) *b);
    //(f (b) - a) *b 下方长方形面积 
	return 0;
}