package com.company;

public class FuncUtils {
    //problem 3
    public static double f(double x){
        double result=Math.pow(x,5.0)*(Math.pow(Math.log(Math.sqrt(x+1.0)),2.0)+2.0)-2.0;
        return result;
    }
    public static double fD2(double x){
        double result=Math.pow(x,5.0)*Math.log(Math.sqrt(x+1.0))/(x+1.0)+5.0*Math.pow(x,4.0)*(Math.pow(Math.log(Math.sqrt(x+1.0)),2.0)+2.0);
        return result;
    }
    public static double getI(double x, double n){
        //bounds are 0 and x, h=x/n
        double h=x/n;
        double sum=0.0;
        for(double k=1.0; k<=n;k++){
            sum+=f((k-1.0/2.0)*h);
        }
        return h*sum;
    }
    public static double getN(double a, double b){
        double result=Math.pow(10.0,3.0)*Math.sqrt(Math.pow(b-a,2)*fD2(b)/24.0);
        return Math.ceil(result);
    }

}