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Simpson's double integral won't work in java

So I had to write an algorithm for the Simpson's double integral so I can find the answer in a much faster manner. I had a guide that showed the steps to follow to write this program. After following this guide and running it in netbeans, I found out that the values coming out of the program where not really close to the real answer. This is the code that I written in java:
//INPUT
double a = 0,b = 1; // Endpoints
int m = 8,n = 4;
double K1 = 0, K2 = 0, K3 = 0;
//OUPUT
//Step 1
double h = (b - a) / n;
double j1 = 0; //End terms
double j2 = 0; //Even terms
double j3 = 0; //Odd terms
//Step 2
for(int i = 0; i <= n; i++){
//Step 3
double x = a + (i * h);
double hX = (d(x) - c(x)) / m;
K1 = f(x, c(x)) + f(x, d(x)); // End terms
//Step 4
for (int j = 1; j < (m-1); j++){
//Step 5
double y = c(x) + (j * hX);
double q = f(x,y);
//Step 6
if (j % 2 == 0){
K2 = K2 + q;
}
else
K3 = K3 + q;
}
//Step 7
double l = (K1 + (2*K2) + (4*K3)) * (hX / 3);
//Step 8
if (i == 0 || i == n)
j1 = j1 + l;
else if (i % 2 == 0)
j2 = j2 + l;
else
j3 = j3 + l;
}
double j = h * (j1 + (2 * j2) + (4 * j3)) / 3;
System.out.println("j = " + j);
}
public static double c(double x){
return x;
}
public static double d(double x){
return 2 * x;
}
public static double f(double x, double y){
return (Math.pow(y, 2) + Math.pow(x, 3));
}
I tried debugging the program several times but I haven't yet found why I am encountering this mistake. If there's any mistake that you find in my code please let me know to see if it fixes it. For the given example, I am getting the value of 0.9069281684027777 instead of having the correct value which is 0.7838542. Thank you for your help. You can also see the guide that I followed to be able to create this program.

I did not check the math, the large error seems to indicate an error in the algorithm implemented. The for-bounds are dubious. And floating point errors exist.
Instead of multiplying a fraction by a running index (which would multiply the floating point approximation error in the fraction), better do:
Instead:
double h = (b - a) / n;
for (int i = 0; i <= n; i++) {
double x = a + (i * h);
do
for (int i = 0; i < n; i++) {
double x = a + i * (b - a) / n;
or
for (int i = 0; i <= n; i++) {
double x = a + i * (b - a) / (n + 1);
The boundary n being a bit unclear to me.

I expect the Histogram to be showed in the range of min and max of my image value ,But it includes bigger values than max-value

I use Conrad open source and I want to compute the histogram of an image. For that first, I found the min and max of my image values and range=max-min and then the lower-limit and upper-bound exactly according to this link https://www2.southeastern.edu/Academics/Faculty/dgurney/Math241/StatTopics/HistGen.htm
Now my problem is that how can the program divide the range according to the bin-Width and how can I assign each image values to each bin-width(classes).
public static int[] computeHistogram2D(Grid2D grid, int bins, int width, int heigth) {
float val = 0;
float max = -Float.MAX_VALUE;
float min = Float.MAX_VALUE;
for (int i = 0; i < width; i++) {
for (int j = 0 ; j < heigth; j++) {
val = grid.getAtIndex(i, j);
if (val > max) {
max = val;
}
if (val < min) {
min = val;
}
}
}
int[] histo = new int[bins];
double[] histof = new double[bins];
float range = max - min;
float lowerLimit = range/(float)bins;
float upperBound = range / (float) (bins -1);
//float binWidth =( upperBound - lowerLimit)/bins;
for (int i = 0; i < width; i++) {
for (int j = 0 ; j < heigth; j++) {
val = grid.getAtIndex(i, j);
int b = (int) ((val - min) / upperBound);
histo[b]++;
histof[b]++;
System.out.println(" intervals " + b );
}
}
System.out.println("maxValgrid2D: " +max + " minValGrid2D: " + min + " binWidth "+ upperBound);
VisualizationUtil.createPlot(histof, "Histogram2D", "intensity", "count").show();
return histo;
}
This is what I got as a result,which seems to be wrong because the max-value of my pic is 21.12
What I expect to get

How to split an integer into individual digits and then square each number?

I want to split an integer into digits and then raise each number to the power 2 and print that out. This is what I have:
int n = 666;
String number = String.valueOf(n);
for (int i = 0; i < number.length(); i++) {
int j = Character.digit(number.charAt(i), 10);
Math.pow(j, 2);
System.out.println(j);
}
The output is only the 666 number.
What is it I'm doing wrong?

Math.pow(j, 2) doesn't modify j, it returns a new value. You should capture the output of Math.pow to a variable and print that

If you want to print sq of individual digits.
int num = 666;
String number = String.valueOf(num);
for (int i = 0; i < number.length(); i++) {
int j = Character.digit(number.charAt(i), 10);
int res = (int) Math.pow((double) j, (double) 2);
System.out.println("digit: " + res);
}

int m = n;
while (m > 0)
{
int digit = m % 10;
System.out.printf("%d\n", Math.pow(digit, 2));
m /= 10;
}
Is this what you want?
Due to Andreas comment which said the order is reversed, I changed the code:
int length = number.length();
for (int i = length - 1; i >= 0; i--)
{
int divisor = (int) Math.pow(10, i);
int digit = n % divisor;
System.out.printf("%d\n", Math.pow(digit, 2));
}
Also I could have written it as:
int length = number.length();
int divisor = (int) Math.pow(10, length - 1);
while (divisor > 0)
{
int digit = n % divisor;
System.out.printf("%d\n", Math.pow(digit, 2));
divisor /= 10;
}

Your code isn't working because you don't actually use the return value of Math.pow().
Math.pow(x, 2) is one way to raise a number to the power of 2, but it is floating-point math, not integer math. Power of 2 means to multiply the number by itself, so x * x is much better.
int number = 299792458; // Speed of light in m/s
for (char ch : Integer.toString(number).toCharArray()) {
int digit = ch - '0';
System.out.println(digit * digit);
}
Or using Java 8 streams:
int number = 299792458; // Speed of light in m/s
Integer.toString(number)
.chars()
.map(c -> (c - '0') * (c - '0'))
.forEach(System.out::println);
OUTPUT
4
81
81
49
81
4
16
25
64

What's the difference when using numeric literal in termination expression of a for statement?

Why does this piece of code:
String value = JOptionPane.showInputDialog("Enter x"); //Input = 100
int x = Integer.parseInt(value);
double result = 1;
for (int i = 1; i <= x; i++) //used variable "x" here
{
result += (x * 1.0) / fact(i);
x *= x;
}
public static int fact(int n) {
int fact = 1;
for (int i = 1; i <= n; i++) {
fact *= i;
}
return fact;
}
work differently from this one?
String value = JOptionPane.showInputDialog("Enter x"); //Input = 100
int x = Integer.parseInt(value);
double result = 1;
for (int i = 1; i <= 100; i++) //and here I used the value "100"
{
result += (x * 1.0) / fact(i);
x *= x;
}
public static int fact(int n) {
int fact = 1;
for (int i = 1; i <= n; i++) {
fact *= i;
}
return fact;
}
The only change that I made was using the value 100 instead of using the variable x in my termination expression!
When I run the first code, I get:
9.479341033333334E7
However, for the second one I always get
NaN
Why?

The difference between the two snippets is this:
for (int i = 1; i <= x; i++) {
vs.
for (int i = 1; i <= 100; i++) {
In the first case, x gets much larger every time! Eventually, it will stop when x overflows and becomes 0, which will be much sooner than in the second case. For an explanation as to why this results in 0 instead of some other random number, see: Why does this multiplication integer overflow result in zero?
In the second case, when i = 34, fact(n) will return 0, so the double division is (0 * 1.0) /0 which results in NaN. Any double, when added to NaN, becomes NaN, which is why the second snippet results in NaN. See: In Java, what does NaN mean?

nested for() loops && using the "i" count from the first loop in the second so i loops just once using the value?

i am trying to not import the math class to use but i am still trying to estimate the constant "e". it is said e= 1+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+.....
these are what i have int at the top
String userInput;
int uIp; // this converts the string into int type
double e = 2;
then i ask some questions then i check to see not zero to exit and non negative to continue
While(uIp >0){
final int endTheLoop = 15;
int factorialNumber = 1;
double e2TheUserInput=0;
for(int i = 2; i < endTheLoop; i++){
for(int j = 1; j < i; j++){
factorialNumber = ((i - 1) * factorialNumber);
}
e = (1/factorialNumber) + e;
e2TheUserInput = Math.pow(e,uIp);
}
}

You are doing integer division(but e is a double right?):
e = (1/factorialNumber) + e;
Correct that to:
e = (1.0/(double)factorialNumber) + e;
It was counting all the loops, but changes are zero according to the integer division. :)
e= 2+(0)+(0)+(0)+(0)+.....

I am not sure what your code is trying to do but if you want to compute exp(x) this is how I would do it.
public static void main(String... args) {
for (int i = -4; i <= 4; i++)
System.out.println(i + ": " + exp(i) + " cf " + Math.exp(i));
}
private static double exp(double d) {
if (d < 0)
return 1 / exp(-d);
double e = 1, term = 1;
for (int i = 1; i < 20 || term > e * 1e-16; i++) {
term *= d / i;
e += term;
}
return e;
}
For large exponents, it more efficient to evaluate the integral powers without using a taylor series.
public static final double E = 2.7182818284590452354;
private static double exp(double d) {
if (d < 0)
return 1 / exp(-d);
long num = (long) d;
double numE = 1;
double mult = E;
while (num > 0) {
if ((num & 1) != 0)
numE *= mult;
num >>>= 1;
mult *= mult;
}
double fract = d - (long) d;
double fractE = 1, term = 1;
for (int i = 1; i < 20; i++) {
term *= fract / i;
fractE += term;
}
return numE * fractE;
}