for mike

#include <iostream>#include <cmath>#include <iomanip>using namespace std;double f(double x);double F(double x);double trapInt();double rombInt();double intPow(double x, int n);double a = 10;double b = 15;int main() {		cout << scientific << showpoint << setprecision(12)			<< "Welcome to the Show!\n\n";		cout << "Symbolic:\t" << F(b) - F(a) << endl;		cout << "Trapezoid:\t" << trapInt() << endl;	cout << "Romberg:\t" << rombInt() << endl;	return 0;}/* returns f(x) for given x */double f(double x) {	return 2.1*log(x) - 3.0*sin(2*x) - 2.7*cos(4.5*x) - 0.3;}double F(double x) {	return 2.1*(x*log(x)-x) + 1.5*cos(2*x) - 0.6*sin(4.5*x) - 0.3*x;}double trapInt() {		double h, sum, x;	int n;		/* symbolic calculation gives that f''(q)<=58.994808 for 10<q<15 */	h = sqrt(0.5e-6 / (5./12. * 58.994808));	n = (int) ceil( (b-a) / h );	//	cout << "trap intervals: " << n << endl;		sum = 0.5 * (f(a)+f(b));		for (int i = 1; i <= n-1; i++) {		x = a + i*h;		sum += f(x);	}		sum *= h;		return sum;}double rombInt() {		int maxRows = 20;	double epsilon = 0.5e-6;	double R[maxRows][maxRows];	double sum;		double h = b - a;	R[0][0] = h/2*(f(a)+f(b));//	cout << R[0][0] << endl;	for (int n = 1; n <= maxRows; n++) {		h /= 2;		sum = 0;				for (int i = 1; i <= intPow(2,n)-1; i+=2) {			sum += f(a+i*h);		}				R[n][0] = 0.5*R[n-1][0]+h*sum;		//		cout << "n = " << n << "\tR[n][0] = " << R[n][0] << endl;		for (int m = 1; m <= n; m++) {//			if ((R[n][m-1]-R[n-1][m-1]) < epsilon)//				return R[n][m-1];			R[n][m] = R[n][m-1];//				+ (R[n][m-1]-R[n-1][m-1])/(intPow(4,m)-1);		}	}		return 999;}double intPow(double x, int n) {	if (n > 1)		return x*intPow(x, n-1);	else		return x;}