I'm toying around with statistics and calculus for a project of mine and I'm trying to find the simplest/fastest way to integrate this formula :   $$\int_{-\infty}^{+\infty} e^{-x^2/2} dx$$   I do not want to use a table. I'm taking this opportunity to get more practice with my new calculus skills It seems that a Taylor series approx is the only way to go   Best Regards
How to prove  $$\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$$
How to see the error messages when I get the white screen of death? Let $\Omega=\mathbb{N}$. For each $E\subset\Omega$ let $N_n(E)$ be the cardinality of the set $E\cap \{1,2,\ldots,n\}$. Define $C=\left\{E: \lim_{n\rightarrow \infty} \frac{N_n(E)}{n} \text{ exists}\right\}$. Show that $C$ isn't a field.  I already know that it isn't closed to finite union of non-disjoint set but I can't see why. I saw a post that somebody said &quot;the set of natural numbers whose first digit is 1 doesn't have this limit&quot;. I'm in trouble to see why this limit wouldn't exists in finite unions. Thanks in advance. Different dependencies for different build profiles Is it possible to have a different set of dependencies in a maven pom.xml file for different profiles?  e.g.  mvn -P debug mvn -P release   I'd like to pick up a different dependency jar file in one profile that has the same class names and different implementations of the same interfaces. What would be the sum of the following series?  $$\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$$  Thanks How can I make the map::find operation case insensitive? Prevent browser caching of AJAX call result It looks like if I load dynamic content using $.get(), the result is cached in browser.  Adding some random string in QueryString seems to solve this issue (I use new Date().toString()), but this feels like a hack.   Is there any other way to achieve this? Or, if unique string is the only way to achieve this, any suggestions other than new Date()? What is the best way to vertically center the content of a div when the height of the content is variable.  In my particular case, the height of the container div is fixed, but it would be great if there were a solution that would work in cases where the container has a variable height as well. Also, I would love a solution with no, or very little use of CSS hacks and/or non-semantic markup. Conditional distributions of the multivariate normal Moving one object causes other to move another (already tried unlinking) General rule for partial fraction decomposition What counter balances gravity here? Lets consider a stone tied to one end of a massless and unstretchable string... Now if i'll start rotating, it will form a conical pendulum &amp; then the equilibrium is achived when the pendulum attains horizontal circular motion.... Now to maintain that state we give a constant force to string.... Here, which force counterbalances gravity? Is it the torque due to applied force cancels out the torque due to gravity?  The angle θ changes from 0 to 90° Using wired and wireless headphones simultaneously? I have 1 android device, 1 wired headphones, 1 wireless headphones, 2 ppl willing to watch film.  When I connect both of headphones only wired work.  Is it possible to use both of headphones simultaneously? How to access blocked sites? I am in Pakistan and  is blocked here. I want to take the Lecture videos from YouTube. In Windows, I was using  to bypass the proxy.   But now, using Ubuntu, I don't know how to bypass the proxy. I found some where that i can bypass the proxy by using putty software. Can you guide me how can I bypass proxy by that? I tried, but I was not able to do so. Kindly tell me some easy method to bypass proxy. I don't want to used websites like accesstoblockedsites.com. How do I reset an old iPod? My daughter gave her little brother her iPod Touch 8g. I have been trying to update the software and would like to get it rest to a factory clean state so I can linked it to the iTunes that already syncs to his iPad.   How can I do a clean up and wipe of everything from an iPod? shade plane with a color function color(x,y) I want to be able to make callouts to JotForm, but they do not support OAuth and username/password is insufficient for their API. ; for reference, here are the 3 auth options:        Authenticate with Query Parameters   Authenticate with HTTP Headers   Authenticate with Javascript SDK      Basically, they provide an API Key and want me to include an apikey parameter in the header. I don't want to hard code it, I don't want to store it as plain text in custom settings/metadata, and this isn't a managed package. Is there any way to securely store/authenticate from Salesforce, ideally using a Named Credential?  I'd love to be able to just have a Named Credential that is just a securely stored, obscured API Key... shorter proof of generalized mediant inequality? On September 29th, I created the  tag for  Today, while checking the tag description, I saw that the  seems to be .  Why is that? Why has the Community user "stolen" the spot as author of the tag? What do you call someone who has extensive knowledge but won't share it? How to fix "sudo: unable to open ... Read-only file system"? The title might not be as descriptive as I would like it to be but couldn't come up with a better one.  My server's file system went into Read-only. And I don't understand why it does so and how to solve it.  I can SSH into the server and when trying to start apache2 for example I get the following :  username@srv1:~$ sudo service apache2 start [sudo] password for username: sudo: unable to open /var/lib/sudo/username/1: Read-only file system  * Starting web server apache2                                                                                                                                                                                                               (30)Read-only file system: apache2: could not open error log file /var/log/apache2/error.log. Unable to open logs Action 'start' failed. The Apache error log may have more information.   When I try restarting the server I get :  username@srv1:~$ sudo shutdown -r now [sudo] password for username: sudo: unable to open /var/lib/sudo/username/1: Read-only file system   Once I restart it manually it just start up without any warning or message saying something is wrong.  I hope somebody could point me into the right direction to resolve this issue.