change the order of integration in $$\int_0^{2a}\int_0^{\sqrt{2ax-x^2}}\frac{\phi'(y)(x^2+y^2)x}{\sqrt{4a^2x^2-(x^2+y^2)^2}}dy\,dx$$  I was able to change the order of integration here to  $$\int_0^a\int_{a-\sqrt{a^2-y^2}}^{a+\sqrt{a^2-y^2}}\frac{\phi'(y)(x^2+y^2)x}{\sqrt{4a^2x^2-(x^2+y^2)^2}}dx\,dy$$ Now i am stuck with the integration here w.r.t $x$. I tried substituting $(x^2+y^2)^2$ with $t$ but then replacing value of $4a^2x^2$ becomes a problem. I was thinking of substituting both $x$ and $y$ as $k\cos\theta$ and $k\sin\theta$ but then $y$ won't be constant w.r.t $x$, so that too I believe is out of the question!
Change the order of integration in:  $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it.    I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex.
I am flying to Tokyo in November, and I have the choice to go direct (paying extra) or transit via Seoul. Is 6 hours transit time enough to leave Incheon airport for a bit to see something of Seoul? It might make my trip more worthwhile to see something of South Korea too. I don't know much about the busyness of the airport around this time, and travel time between the airport and the city, so that's why I am asking. I need to run Firefox browser from terminal. Browser works fine, but terminal still waits for Firefox to return and if I do CTRL+C, it terminates Firefox. How to run command to make Firefox work independently from terminal? Documents required by Indian citizens wishing to travel to Nepal Prepositional Phrase - confused - at or in I want to unwrap a label which has a transparent area Regular Expression to split on spaces unless in quotes I would like to use the .Net Regex.Split method to split this input string into an array. It must split on whitespace unless it is enclosed in a quote.  Input:  Here is "my string"&nbsp;&nbsp;&nbsp;&nbsp;it has "six&nbsp;&nbsp;matches"  Expected output:   Here is my string it has six&nbsp;&nbsp;matches   What pattern do I need? Also do I need to specify any RegexOptions? Sequence of differentiable functions Let $f_n$ be a sequence of differentaible functions on $[0,1]$ to $\mathbb{R}$ converging uniformly to a function $f$ on $[0,1]$, Then    $f$ is differentiable and Riemann integrable there $f$ is uniformly continuous and R-integrable $f$ is continuous, need not be differentiable on $(0,1)$ and need not be R-integrable on $ [0,1]$, $f$ need not be continuous.   Well I think 2 is only correct statement  as every $f_n$ are differentiable on $[0,1]$ hence uniformly contnous, and as they converge uniformly to $f$ on $[0,1]$ so $f$ is uniformly continuous and every continuous function is rieman integrable..Am I correct? dollar-terminated strings In my assembly language class, our first assignment was to write a program to print out a simple dollar-terminated string in DOS.  It looked something like this:  BITS 32     global _main  section .data     msg db "Hello, world!", 13, 10, ’$’  section .text _main: mov ah, 9 mov edx, msg int 21h ret   As I understand it, the $ sign serves to terminate the sting like null does in C.  But what do I do if I want to put a dollar sign in the string (like I want to print out "it costs $30")?  This seems like a simple question, but my professor didn't know the answer and I don't seem to find it using a google search. is there a better way to do this XML scraping task in R? What's the last character in a file? I just read the answers to  and everyone said to delete the last character. My question is,  isn't the eof character the last one? Installing Elementary OS - will it automatically be added to the Grub menu? I currently have Windows 7 and Linux Mint installed.  When my PC starts up, it shows me the Grub menu, it shows an entry for Mint Linux and the Windows boot menu.  I am wondering, if I was to install Elementary OS, would it be automatically added to grub or do I have to put some command in the terminal?  I also want to ask, when I boot from my Elementary OS cd, and install it, just before it finishes, it shows some kind of error saying some error about cannot install to grub or something, I've tried installing to a separate partition and alongside "Them", but had no luck.  I'm really new to Linux, and want to keep my Mint Linux and Windows 7 because I have files on them. Recommended books for advanced undergraduate electrodynamics 3rd iterate of a continuous function equals identity function If $ f: \mathbb{R} \to \mathbb{R} $ is continuous, and $\forall x \in \mathbb{R} :\;(f \circ f \circ f)(x) = x  $, show that $ f(x) = x $.  The condition that $f$ is continuous on $\mathbb{R}$ is crucial for the proof. I can find functions such as $\displaystyle\frac{x-3}{x+1}$ that satisfies  $ (f \circ f \circ f)(x) = x $. I have tried to negate the conclusion to see if there's a contradiction, but got stuck. Diffeomorphism group of the unit circle I am given to understand that the group of diffeomorphisms of the unit circle, $\operatorname{Diff}(\mathbb{S}^1)$, has two connected components, $\operatorname{Diff}^+(\mathbb{S}^1)$ and $\operatorname{Diff}^-(\mathbb{S}^1)$, the diffeomorphisms that preserve or reverse the canonical (counterclockwise) orientation, respectively.  Question 1: How does one prove that?  Question 2: Given $\Phi, \Psi \in \operatorname{Diff}^+(\mathbb{S^1})$, can one construct an explicit path joining them?  I'd be satisfied already with a proof that we can join $\Psi, \Phi \in \operatorname{Diff}^+ (\mathbb{S}^1)$, without giving the path explicitly. I tried the obvious path, $t \mapsto \dfrac{t\Phi + (1-t)\Psi}{|t\Phi + (1-t)\Psi|}$, but that doesn't seem to work.  Thanks. What tool do you use to monitor your servers? For a more comprehensive list of monitoring tools and their features, check out .   As the question states, what are the most commonly used tools used for this task and what are their strengths and weaknesses? Microsoft Edge missing in Start menu and pins Note: People have seem to have had issues doing this in Windows 10 pro, this could be because of Windows Updates. If the solution does not work, please use "Refresh your PC"  I have just upgraded to Windows 10 and had to switch to a Microsoft account while setting up Cortana.   Along the process, it asks me to sign out and sign back in, which I do. Then after signing back in, Microsoft Edge is missing. From the taskbar, and the "All Apps" section of the start menu.   This only occurs AFTER I have added my Microsoft account. And the only way is to open a .HTML file like this one:    (The name was from my Windows 7 Dualboot Install)  and please don't say "Just open the HTML file!" I need a proper solution to this. I am trying to find a story where a children's nursery turns into a jungle I read this short story(I believe it was under novella length, but I could be mistaken) a while back, and I am trying to identify the title for a friend.   Plot:      Parents(male and female) get a computer aided/holographic nursery for their children. The mother becomes increasingly agitated as the children withdraw more. The children are barely even featured in the story, and the ending concludes with lions possibly eating the parents.   Publishing date: Years ago.   Tech level: Seemingly functional AI, not much more. Case insensitive 'Contains(string)' Is there a way to create synchronization profiles for Google Chrome? For example I want to tag some of my browsers as "home browser"s and others as "work browser"s and I want:   my bookmarks to be synced with all browsers, my extensions to be synced only within browsers of the same type (home with home, work with work) I accidentally changed /var owner/group to my username and then changed it back to root, but not all the /var folders' owners are root, so is there anyway to change back owner/group of files/folders to default state?  Or at least those files/folders that are created by packages?