#### [Homework help] Why is my integral function not entirely accurate?

Ok, so I'm working on the following assignment:

Create a class and call it Assignment3_2. Write a method f and a method integral which comply to the following specifications:

f(x : double) : double
returns the squareroot of x

integral(start : double, end : double, res : double) : double
returns (f(start) + f(start+step) + ... + f(bg)) * res

(in other words, if f(x) would just return x, instead of the squareroot of x, you would get the integral from start to end with the specified resolution)
Here's what I created:

Code:
```import java.lang.Math;

public class Assignment3_2 {

private static double f(double x) {

x = Math.pow(Math.E, (Math.log(x)*0.5));

return x;

}

private static double rie_sum(double start, double end, double res){

double sum=0;
double current = start;

while(current <= end){

sum += f(current);
current += res;

}

return sum;

}

public static double integral(double start, double end, double res){

double integral = res * rie_sum(start, end, res);

return integral;

}

public static void testAssignment3_2(){

System.out.println("f(3.0) == 1.7320508076 is " + (Math.abs(f(3.0) - 1.7320508076) <= 1E-9));
System.out.println("f(9.0) == 3.0          is " + (Math.abs(f(9.0) - 3.0) <= 1E-9));
System.out.println("integral(0,50,1)     == 239.0358082329 is " + (Math.abs(integral(0.0,50,1) - 239.0358082329) <= 1E-9) + " Error: " + (integral(0.0,50,1) - 239.0358082329));
System.out.println("integral(0,50,0.1)   == 235.3421927538 is " + (Math.abs(integral(0.0,50,0.1) - 235.3421927538) <= 1E-9) + " Error: " + (integral(0.0,50,0.1) - 235.3421927538));
System.out.println("integral(0,50,0.01)  == 235.7374085139 is " + (Math.abs(integral(0.0,50,0.01) - 235.7374085139) <= 1E-9) + " Error: " + (integral(0.0,50,0.01) - 235.7374085139));
System.out.println("integral(0,50,0.001) == 235.7057893690 is " + (Math.abs(integral(0.0,50,0.001) - 235.7057893690) <= 1E-9) + " Error: " + (integral(0.0,50,0.001) - 235.7057893690));

}

public static void main(String[] args) {

System.out.println(integral(0.0, 50, 1));
System.out.println(integral(0.0, 50, 0.1));
System.out.println(integral(0.0, 50, 0.01));
System.out.println(integral(0.0, 50, 0.001));
System.out.println();
testAssignment3_2();

}
}```
You'll notice there's a method called testAssignment3_2 in there, this method was provided by the assignment and it's meant for checking if the integral function is accurate.

As you've probably guessed, my integral function is not accurate. The weird thing is: it's pretty accurate, but not enough. Running my code gives:

Code:
```239.03580060352076
235.342191990834
235.73740843760655
235.7057893613778

f(3.0) == 1.7320508076 is true
f(9.0) == 3.0          is true
integral(0,50,1)     == 239.0358082329 is false Error: -7.6293792403703264E-6
integral(0,50,0.1)   == 235.3421927538 is false Error: -7.629659819485823E-7
integral(0,50,0.01)  == 235.7374085139 is false Error: -7.62934462272824E-8
integral(0,50,0.001) == 235.7057893690 is false Error: -7.622190878464608E-9```
The error margin gets progressively smaller with an increasing resolution and I have absolutely zero clue why.

I know this kind of a complicated problem to expect someone to help me with free of charge, but if one of you java guru's could perhaps take a look at this, I'd be EXTREMELY grateful.