public abstract class RFunc{

public abstract double evaluate(double x);

public double bracketRoot(double a, double b, double maxErr){

double fl = evaluate(a);

double fu = evaluate(b);

double upper = b;

double lower = a;

double x = 0.0;

double fx;

//System.out.println("delta = " + (upper - lower));

while((upper-lower) > maxErr){

x = (upper+lower)/2;

//System.out.println("x = " + (x));

fx = evaluate(x);

if(fx == 0) return(x);

else if((fx>0) && (fu>0)){ upper = x; fu = fx;}

else if((fx<0) && (fu<0)){ upper = x; fu = fx;}

else { lower = x; fl = fx;}

}

return(x);

}

public double defIntegral(double a, double b, int nsteps){

int i;

double h = (b-a)/nsteps;

double x = a;

double sum = (evaluate(a)+evaluate(b))/2;

for(i=1;i<nsteps;i++){

x += h;

sum += evaluate(x);

}

return(sum * h);

}

}