Multiple Integral Puzzle
$ \int_1^2\int_1^2 \int_1^2 \int_1^2 \frac{x_1+x_2+x_3-x_4}{x_1+x_2+x_3+x_4}dx_1dx_2dx_3dx_4 $
Everytime, I read about blackbody, I always get confused at the point where it is written     Under thermal equilibrium conditions , the blackbody radiation depends only on temperature. ..... . At equilibrium , electromagnetic waves bounce around with the walls of the cavity.   What is this equilibrium all about? Why is it important here?? If there is thermal equilibrium, why does the body radiate?? Please help. How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$? When connected to the Internet, the system checks if it's in a walled garden, which is simply trying to connect to Google. If it fails, in Android 5, there'll be an exclamation mark on the WiFi icon or signal icon.   In some situations, this is annoying. Say, in China, Google is blocked, the exclamation mark will always be there, which is meaningless.  How can I disable this check, and make the system assume, connected WiFi/mobile data is connected Internet? What is a "static" function in C? The question was about plain  functions, not  static methods, as clarified in comments.  I understand what a static variable is, but what is a static function?  And why is it that if I declare a function, let's say void print_matrix, in let's say a.c (WITHOUT a.h) and include "a.c" -  I get "print_matrix@@....) already defined in a.obj", BUT if I declare it as static void print_matrix then it compiles?  UPDATE Just to clear things up - I know that including .c is bad, as many of you pointed out. I just do it to temporarily clear space in main.c until I have a better idea of how to group all those functions into proper .h and .c files. Just a temporary, quick solution. How can I read a large text file line by line using Java? Is it possible to run three versions of Google Chrome? How might I run 3+ versions of google chrome so I can log into to 3 different google accounts.  More specifically I am looking to have separate icons in the dock for the 3 separate running applications.  How might I run duplicate and or copy versions of the same application.  The following  by Mark works for a lot of applications but not for Google Chrome.  It appears the following might work . How to format table with long column head entries? Huge close votes review queue on Stack Overflow Apply for Schengen visa in a third country Can a Kenyan citizen studying in Russia and temporarily visiting family in Kenya apply for a Schengen visa in Nairobi and not in Russia, where he has his residence? What is the difference between "till" and "until"? What is the difference between till and until?    When to use till or until? Please explain with examples. Is my processor 64 or 32 bit? In MTG, what happens when a player loses in multiplayer? In Magic: The Gathering, the rules for a player losing in a multiplayer game are quite complex, so I'd like to try to understand them by example. I would be happy to ask each of these situations as a separate question if that is preferred, but they all seem related, and I would love to have one place to look up all of these answers.  Let's say I'm playing with two friends, Bob and Chloe, in a simple free for all. Unfortunately, I lose. When I lose, suppose the following:   I controlled an  which has exiled Bob's , does he get his bear back? I have a  on the stack targeting Chloe, does Chloe take the 2 damage still? Earlier in the turn I cast  to prevent damage to one of Bob's . If it later takes 3 damage, will that damage be prevented? Something I controlled gave Bob a 1/1 soldier token. What happens to the token? Something Chloe controlled gave me a 1/1 soldier token. What happens to the token? I had a  enchanting one of Bob's army of . What happens to the bear? I had also played  on Bob's final . What happens to the last bear? Chloe had  my . What happens to the Clone? Are there any other situations specifically addressed by the rules? So I've got a file with loads of simple objects. This will later be used to cut out these shapes out of plastic. So, using the material optimally is of outmost importance. I was wondering if there is any script or plugin that could automaticly arrange the objects within the artboard so they could fit best. Custom Adapter for List View In ZFC set theory, every element object is a set. We know or feel that if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.  My question is: Why if $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set? Is there an exact command for restarting GNOME Shell in Ubuntu 20.04 corresponding to Alt + F2 + 'r' + Enter? Is there a way to restart GNOME Shell other than by using Alt + F2, R + Enter? With respect to the question, I have gone through , but I didn't get what I was looking for. I am looking for a command which exactly does what Alt + F2, r + Enter do. Please note that I am not willing to do the gnome-shell -- replace command... I did check both the things Alt + F2,r Enter and gnome-shell --replace... There is a lot of difference, I found... Is a "split plot" ANOVA with two factors the same as two-way ANOVA with repeated measures in one factor? Is a "split plot" ANOVA with two factors identical to two-way ANOVA with repeated measures in one factor? if not, what is the distinction? Printing pointers in C I was trying to understand something with pointers, so I wrote this code:  #include &lt;stdio.h&gt;  int main(void) {     char s[] = "asd";     char **p = &amp;s;      printf("The value of s is: %p\n", s);     printf("The direction of s is: %p\n", &amp;s);      printf("The value of p is: %p\n", p);     printf("The direction of p is: %p\n", &amp;p);      printf("The direction of s[0] is: %p\n", &amp;s[0]);     printf("The direction of s[1] is: %p\n", &amp;s[1]);     printf("The direction of s[2] is: %p\n", &amp;s[2]);      return 0; }   When compiling it with gcc I get these warnings:  $ gcc main.c -o main-bin -ansi -pedantic -Wall -lm main.c: In function ‘main’: main.c:6: warning: initialization from incompatible pointer type main.c:9: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char (*)[4]’ main.c:11: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char **’ main.c:12: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char ***’   (The flags for gcc are because I must be C89)  Why incompatible types of pointer? Isn't the name of an array a pointer to it's first element? So if s is a pointer to 'a', &amp;s must be a char **, no? And why do I get the other warnings? Do I have to cast the pointers with (void *) in order to print them?   And when running I get something like this:  $ ./main-bin The value of s is: 0xbfb7c860 The direction of s is: 0xbfb7c860 The value of p is: 0xbfb7c860 The direction of p is: 0xbfb7c85c The direction of s[0] is: 0xbfb7c860 The direction of s[1] is: 0xbfb7c861 The direction of s[2] is: 0xbfb7c862   How can the value of s and it's direction (and of course the value of p) be the same? Let $A$ and $B$ be $m \times n$ and $n \times m$ real matrices.  I proved that if $\lambda$ is a nonzero eigenvalue of the $m \times m$ matrix $AB$ then it is also an eigenvalue of the $n \times n$ matrix $BA$. But I am having trouble finding an example showing that this need not be true if $\lambda=0$  Thank you in advance how to prove $437\,$ divides $18!+1$? (NBHM 2012) I was solving some problems and I came across this problem. I didn't understand how to approach this problem. Can we solve this with out actually calculating $18!\,\,?$