Let $0 &lt; r &lt; 1$. Compute $$\frac{1}{2 \pi} \int_0^{2 \pi} \frac{1 - r^2}{1 - 2r \cos(\theta) +r^2}d\theta$$ The hint is rewrite this integral as a complex line, but I still don't know how to to it
How do you integrate $\int \frac{1}{a + \cos x} dx$?  Is it solvable by elementary methods?  I was trying to do it while incorrectly solving a homework problem but I couldn't find the answer.  Thanks!
Can we have a red/status tag for "obsolete"? Given the changes that have been rolled out on Meta for the new close hold reasons, we've lost "too localized" here on meta.  However, "too localized" has a genuine use on meta (which is part change management system) to indicate those things which are truly obsolete (as evidenced by the text of the old close reason "refers to a specific point in time").  That said, there are things that are obsolete on meta, but we have no way of indicating that other than an "off topic" closure, which really sends the wrong message.  To mitigate that, I'd like a status-obsolete tag for meta sites which meta diamonds can apply to posts that have been made obsolete by other changes that were made to the system afterward. The Problem  Accessing my site over https (the only protocol allowed) I get the content, but none of the CSS, images etc.  Drupal is creating pages in response to https requests that include http links to these resources, but it should be using https.  What I've done  I have copied a site to a dev server. The site loads and basically works fine - I can log in etc. It's just that all the links drupal generates are http. The site I've copied it from also runs over https. The site does not exist on http (it would just get a Forbidden error). I've drush cc all.  So Apache's working - I can access the site. .htaccess is working (clean urls work, for example).  I'm using SNI to access the site because the server has other vhosts too, but I'm only accessing the site using the latest Firefox (and as it's a dev site and I'm the only dev, nobody else will use it).  I've done this dozens of times and am quite stumped! Why does Drupal not notice that the request came over https?  The fix  Turns out that .htaccess has this to say:   /* Base URL (optional).                                                          If Drupal is generating incorrect URLs on your site, which could             be in HTML headers (links to CSS and JS files) or visible links on pages     (such as in menus), uncomment the Base URL statement below (remove the       leading hash sign) and fill in the absolute URL to your Drupal installation.    Sure enough, putting $base_url = 'https://example.com'; fixed it.  But why is this necessary? say by has the meaning of      6. indicating the period in which something happens: ‘this animal always hunts by night’   Then do we need to say, ‘Why does the sky glitter by night?’ And can’t we say, ‘Why does the sky glitter at night?’?   If we can use both, what’s the difference between the two? Are there gotchas using varargs with reference parameters I have this piece of code (summarized)...  AnsiString working(AnsiString format,...) {     va_list argptr;     AnsiString buff;      va_start(argptr, format);     buff.vprintf(format.c_str(), argptr);      va_end(argptr);     return buff; }   And, on the basis that pass by reference is preferred where possible, I changed it thusly.  AnsiString broken(const AnsiString &amp;format,...) { ... the rest, totally identical ... }   My calling code is like this:-  AnsiString s1, s2;     s1 = working("Hello %s", "World");     s2 = broken("Hello %s", "World");   But, s1 contains "Hello World", while s2 has "Hello (null)". I think this is due to the way va_start works, but I'm not exactly sure what's going on. I have a virtual machine running ubuntu and I am trying to host some files on ubuntu and map the drive in windows PC.  Following the steps , I am able to see (from windows) the "work" folder after typing in \ubuntu_ip. But when trying to access or map it with "svc_acct" from windows, I get "0x80070043 error the network name cannot be found". I guess I am not accessing correctly from windows.   SAMBA config below (svc_acct is an account set up under linux). When accessing the folder from windows, I get prompted for username/password. Not sure what credential to type in exactly.  samba config: [work] path = /home/svc_acct/work valid users = svc_acct available = yes read only = no browsable = yes public = yes writable = yes force user = svc_acct create mask = 0777 directory mask = 0777   UPDATE:  All I did to resolve this is by changing samba config's path from path = /home/svc_acct/work to path = /home/svc_acct following  post  (last sentence). Then no more prompt for password in windows when I try to click into the folder. Thanks to @sancho.s for suggesting the link. How is (p ∧ q ∧ ¬r) ∨ (p ∧ ¬q ∧ ¬r) ≡ (p ∧ ¬r) ∨ (¬q ∧ q)? Is it really distributive property? The recent user profile tab name change - from "activities" to "all actions" - was not accompanied by a hyperlink update from ...?tab=activities... to ...?tab=allactions...    Click on the "posts edited" link to see the 404-error. Any way to send a personal message to another user? Resampling GeoTIFF images to same resolution using QGIS I have two geotiff images that I would like to resample the same resolution. If I use ArcGIS Desktop this is easy to do but how do I do this using QGIS? Skewness, kurtosis and how many standard deviations values are from the mean As is well known for the normal distribution, 68% of the probability mass is within one standard deviation of the mean, 95% within two standard deviations and 99.7% within 3 standard deviations.   However, I have some empirical distributions that are leptokurtic and negatively skewed. In such circumstances is there a formula based on their higher-order moments to calculate how much of the probability mass is within so many standard deviations of the mean?   I have a measurement and would like to give some sense of how far it is from the midpoint (mean or some other measure of central tendency).  Can this be done? PNG figures in black and white I'm trying to include a png figure and it works when I see it in dvi, but the ps comes in black and white.  If I compile directly to pdf there is no problem. However I'm using psTricks for a different figure, so I need to use ps first.  Any suggestions? When would you use a voltage regulator vs a resistor voltage divider?  Are there any uses for which a resistor divider is particularly bad? Solving the diophantine equation $y^{2}=x^{3}-2$ It is known that the diophantine equation $y^{2}=x^{3}-2$ has only one positive integer solution $(x,y)=(3,5)$. The proof of it can be read from the book "About Indeterminate Equation" (in Chinese, by Ke Zhao and Sun Qi). But the method I have known of solving this problem is algebraic number theory.  My question:      Does there exists an elementary method for solving the diophantine equation $y^{2}=x^{3}-2$?   I have gotten an elementary method by the assumption that "$x$" is a prime. That is, we can get a conclusion from the equation that $3\mid x$. Since $x$ is a prime we get the only solution $(x,y)=(3,5)$. But if $x$ is not a prime, the answer seems to be difficult.  Thank you for your help. Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$ Evaluating $$\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$$   I had read the , but it doesn't work. How to automatically keep user remembered in Devise Adding items to page template dropdown on Page Edit Screen I am developing a WP theme with MVC approach. It only have index.php, functions.php and styles.css on the parent directory. So, I do not want to place page templates on it rather then I want to programmatically provide them from View classes while functionality from edit screen stays the same.   Users need to have page templates select option on the edit screen. How do I successfully add Items to the template dropdown?  I tried to hook into  filter.   Example code:  add_filter( 'theme_page_templates', function($templates){      $templates['my-page-template.php'] = "My Page Template";      return $templates;  });   This does not work because of the use of  on the filtered array, which removes the added page template item. I don't understand why this function is used. It seems you can only remove page template from the list but can not add a new one using the given filter.  Is there any other way around? Already I have lost all hope of looking at late answers etc. It's just a parade of meh. I can't make any kind of intelligent decision because I can't see the other answers to the question, for instance. There's no Looks Good, only Skip, and those feel different to me. So I've been more interested in .  But people keep approving crap while I'm looking at it. Two or three "the post was already approved; please visit to edit" and I'm just "screw this whole thing".  Can we do something like one reject bounces all existing votes: you need three approves in a row? Because a lot of people are stupidly approving and actually driving me away from the queue.    Note this is less about letting bad edits through and more about keeping reviewers motivated. What does the human body use oxygen for besides the final electron acceptor in the electron transport chain? My biology teachers never explained why animals need to breathe oxygen, just that we organisms die if we don't get oxygen for too long. Maybe one of them happened to mention that its used to make ATP. Now in my AP Biology class we finally learned the specifics of how oxygen is used in the  due to its high electronegativity. But I assume this probably isn't the only reason we need oxygen.   What other purposes does the oxygen we take in through respiration serve? Does oxygen deprivation result in death just due to the halting of ATP production, or is there some other reason as well? What percentage of the oxygen we take in through respiration is expelled later through the breath as carbon dioxide? How does the Performance Index work? In one of Dota2's recent patches, Valve has added a new feature called "Performance Index" visible in your own in-game profile.  It is not clear how it works. Is there any information available, what "performance" it monitors?  Does it rely on K/D, K/D/A, Gold per minutes, Experience per minute, or all of them? How to copy files into /usr/local/? (permission denied) I'm still a little new to Ubuntu and was wondering how I can copy files, in this case Aptana Studio, to /usr/local/ without being denied.   Is there a way to do it in terminal? Or a way to allow myself permission?  I should add that I am using 10.10 Desktop edition, not server.