probability – What does "X" mean at the bottom of the integer $ operatorname {E} [X]= int _ { mathbb {X}} xf (x) , dx $?

Section 2.2.7 of "Machine Learning: A Probabilistic Perspective of Kevin Patrick Murphy" gives this formula for the expected value.

$ { displaystyle operatorname {E} (X) = int _ { mathbb {X}} xf (x) , dx.} $

there is an X at the bottom of the integral symbol. What is it? X do you mean here? Does it mean "the domain of the definition", "support" or something else?

time counter up to an int

My question is therefore how can I create a counter that counts in an integer type. I can not use a float or a double. I need to create an int variable, which counts up to.

How to integrate $ int e ^ {arctan (x)} $? [on hold]

How to integrate $ int e ^ {arctan (x)} $?

The problem I am trying to solve is
$ frac {d} {dx} int ^ 1_0 e ^ {arctan (x)} $ and $ frac {d} {dx} int ^ x_0 e ^ {arctan (x)} $

but I can not even solve the beginning of these equations.

c # – CAST (scope_identity () AS int) returns an incorrect MS SQL value

I have been developing for a long time a software which, after executing SQL INSERT using CAST (scope_identity () AS int) - returned the new serial number like this: EndID = (Int32) cmd.ExecuteNonQuery ();

It won't work this morning. The value returned is either 1 or 2, even though the record number created is greater than 5000. Don't know what happened? Why is it malfunctioning?

The code part:

_MSSQLOperation_command = "INSERT INTO (" + goals + ") (" + targetfield + ") VALUES (" + fields value + ")" + "SELECT CAST (scope_identity () AS int)";

SqlCommand cmd = new SqlCommand();
cmd.Connection = _myMSSQLConn;            
cmd.CommandType = CommandType.Text;
cmd.CommandText = _MSSQLOperation_command;

...
cmd.Parameters.AddWithValue("@" + targetField_intoValue(i, 0), times); 
...
EndID = (Int32)cmd.ExecuteNonQuery(); 

Convert Int to currency

I am trying to set up a clock in C # that displays a dollar value (AUD).

I have acquired the following code and modified:

 private void Form1_Load(object sender, EventArgs e)
        {
            int CalculateTimeInMinutes(string input)
            {
                DateTime time = DateTime.Parse(input);
                int CalculateTimeInminutes = (CalculateTimeInMinutes / 100m).ToString("C2");
                Console.WriteLine((int)(time - time.Date).TotalMinutes);
                return((int)(time - time.Date).TotalMinutes);
            }
            }
        }

I return error message CS0019 "The operator" / "can not be applied to operands of type" group of methods "and" decimal ". Can any one provide assistance? More references here: https://codereview.stackexchange.com/a/ 229939/210530

thank you,
Samuel

$ int sin ^ 2 (x) < int | sin (x) | $ [on hold]

I have the question to prove it $ int sin ^ 2 (x) < int | sin (x) | $ between points $ a $ and $ b $ or $ a <b $. I can not understand.

Thank you for any help!

$ int (f) ^ n , textrm dx $ where $ f $ is a polynomial and $ n $ is a positive integer

Besides the enlargement of the integrand, is there a general method for solving the indefinite integrals of the form? $ int (f) ^ n , textrm dx $ or $ f $ is a polynomial and $ n $ is a positive integer? For example, $$ int (x ^ 2 + x) ^ {100} , textrm dx? $$

calculation and analysis – Help with an undefined integral unresolved! $ int ! r ln left (r right) sqrt {ar + {b} ^ {2} + {r} ^ {2}} , { rm d} r $

I really need to solve this indefinite integral:

$ int ! r ln left (r right) sqrt {ar + {b} ^ {2} + {r} ^ {2}} , { rm d} r $

It sounds a lot more complicated than it seems. I found an integral table with
an integral resembles my integral, and the solution involves Polylogs. The link of the full table is below:

http://www-elsa.physik.uni-bonn.de/~dieckman/IntegralsIndefinite/IndefInt.html

Whoever is ready to take up this challenge and help with this integral?

Thank you very much in advance

Int (x / y) * What is it?

I work with drawing code on a screen size x and need to calculate the width of the bottom that will go behind y squares of width equal to the screen.

For example, if the screen has a width of 101 pixels and I want to draw 10 squares of equal width, I have to calculate the value 100 because that will be the total width of the 10 squares.

I know I can get this value using

Int(screenWidth/numSquares)*numSquares

I have to calculate this value several times in several places in the code.

Is there a name for this operation? I want to create an extension or function for her and I can not give her a good name.

Is there a more efficient way to do it?

Is this a good place to ask this question? If no, where is it?

complex analysis – different solution for the same contour integral $ int_ {0} ^ { infty} frac { cos (x)} {1 + x ^ 2} dx $

This question may be silly, but I am quite puzzled by this problem.
In this exercise, I have to solve the next integral

$ int_ {0} ^ { infty} enac { cos (x)} {1 + x ^ 2} dx $

that I will call $ A $ from now on. Since $ f (x) = f (-x) $ I conclude $ A = 1/2 int _ {- infty} ^ { infty} frac { cos (x)} {1 + x ^ 2} dx $

now I can switch to the complex variable $ z $ and rewrite $ cos (z) $ as $ frac {e ^ {iz} + e ^ {- iz}} {2} $ and get

$ 1/4 int _ { gamma} frac {e ^ {iz} + e ^ {- iz}} {1 + z ^ 2} dz $

or $ gamma $ is the upper half circle of radius $ r $. Then I can evaluate the residue for $ z = i $ (the ray will eventually tend to infinity) and via Lemma from Jordan, I get

$ A = pi / 4 (e ^ {- 1} + e) ​​$

Now, my teacher solved this integral in a very similar way, but he went from

$ A = 1/2 int _ {- infty} ^ { infty} frac { cos (x)} {1 + x ^ 2} dx = 1/2 int _ {- infty} ^ { infty} frac {e ^ {ix}} {1 + x ^ 2} dx $

I have tried to piece together the steps that lead me from one form to the other but I am not able to do it. What do I forget here?

Thank you in advance to all those who will participate.