How do you compute this integral? $$\int_0^{2\pi} e^{R \cos t} \cos(\sin t+3t)dt \quad R&gt;0.$$ My friend sent this to me the other day, but have not made much progress so far. Maybe using line integrals would be the easiest way to go about, since it looks like it will get messy very fast. He says that the answer should be $0$ which makes me think that this thing is symmetric over $\pi/2$, but not sure.
Calculate: $$\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$$ My try: $\displaystyle\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)dt\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\cos(\mathfrak{I\textrm{z}}+3(-i\log z)dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}}^{(\mathfrak{I\textrm{z}}+3(-i\log z))i}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}}z^{3}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}R}z^{3}dz$ and there is nothing here that is not holomorphic, therefore according to Cauchy theorem it must be exactly $0$.
What is currently the best way to get a favicon to display in all browsers that support Favicons? "std::endl" vs "\n" Many C++ books contain example code like this...  std::cout &lt;&lt; "Test line" &lt;&lt; std::endl;   ...so I've always done that too. But I've seen a lot of code from working developers like this instead:  std::cout &lt;&lt; "Test line\n";   Is there a technical reason to prefer one over the other, or is it just a matter of coding style? Python does not find packages installed without Anaconda The Android OS monitors the power consumption of running apps and hardware (display). As you may guess, this is a useful feature as it allows to track down energy greedy apps.  Is there an application that would do such monitoring on Mac OS?  It should calculate the percentages of the charge that an application/process/hardware has used.  I use plenty of little software that runs in the background permanently. It would be nice to know if such little helpers drain the battery significantly. Imagine this directory structure:  app/    __init__.py    sub1/       __init__.py       mod1.py    sub2/       __init__.py       mod2.py   I'm coding mod1, and I need to import something from mod2. How should I do it?    I tried from ..sub2 import mod2 but I'm getting an "Attempted relative import in non-package".  I googled around but found only "sys.path manipulation" hacks. Isn't there a clean way?      Edit: all my __init__.py's are currently empty    Edit2: I'm trying to do this because sub2 contains classes that are shared across sub packages (sub1, subX, etc.).  Edit3: The behaviour I'm looking for is the same as described in  (thanks John B) How to get more info out of the uninformative Windows 8 BSOD? Why is triple-DES using three different keys vulnerable to a meet-in-the-middle-attack? Among other sources,  states that triple DES using three seperate keys (k1, k2, k3) is vulnerable to meet-in-the-middle-attacks, while triple DES using only two keys (k1, k2, k1) is not.  Why is this attack possible if all the keys are different, but not if the first and the third are the same? Installing from source - do I need to keep the extracted tarball directory If I'm installing from source, do I need to keep the extracted tarball directory?  So if I download the git tarball. I then do:  tar -xvzf git.tar.gz   This will create a git.x.x. directory, into which I cd, then run ./configure etc. Once I'm done with this process, and git, or whatever is installed, do I need to keep the original git.x.x extracted directory, or is that just used for compiling the program?  I'm somewhat confused by all the directories, and folders used for programs. So it looks like Stack Exchange now supports HTTPS (to some extent). Which is awesome! But there are a few problems, the main one being that some content is delivered over the CDN, which is plain HTTP. This causes browsers to complain about "unsecured content": How do I get permissions to delete files on Windows 7? I updated my laptop's OS from Windows XP to Windows 7. There are some leftover files from Windows XP on the computer now. If I try deleting them I get the following error:     You need permission to perform this action.      You require permission from S-1-.... to make changes to this folder.   What's weird is that I am logged in with the only user account on this machine and I have administrator privileges. I tried turning UAC off, but I still can't delete the files.  How can I force removal of these files? How can I cast int to enum? How can an int be cast to an enum in C#? Was Thanos really committed or just a hypocrite? The title is extremely vague, because this question contains HEAVY spoilers for Avengers: Infinity War, specifically the very last scenes of the movie. I can't reasonably put the entire question in spoiler tags, so consider this your warning.  At the end of the movie, Thanos pretty much wins. He gets all the Infinity Stones, Gamora and Vision have been brutally murdered, and the rest of the cast completely beaten. Nobody could stop him. So he executes his plan.  As far as I know (unless I missed something), his plan is to eradicate exactly half of all mortals in the universe, and from his own words, in a fair lottery (random chance), without taking into account a person's wealth, social status, or anything else. Pure chance decides whether you are sacrified for the greater good or live through this greater good (according to him).  During the movie, Thanos and one of his underling (Ebony Maw) say themselves that being sacrified is an honor and should be appreciated. As you would expect, most people do not appreciate being sacrified.  At the end of the movie, Thanos uses all 6 stones to do a finger snap, deleting half the universe.  The question is: Did he exclude himself from the targets? Was there a 50% chance that Thanos himself would disappear right there?  As far as I know, this is not explicitly answered in the movie itself. I am looking for similar situations in the comics (or in the movie if I happened to miss something) where you could know, or have an educated guess, as to Thanos being the kind of person who follows through to the end, even if it means dying, or the kind of person who gets scared of death when it comes down to it, and comes off as an hypocrite.  Some people also mentioned his "deal" with Strange would make him spare Tony from the snap too. I'm also wondering about that, if there is a link between the two, but it's not the focus of the question.  The reason I'm wondering is that Thanos seems to me like a very extreme utilitarist. Even though he might be wrong about the value of his plan (Do the remaining half really become happy?), in-universe it seemed successful at least once (Gamora's home planet), so his reasoning is not bad, even if the premise might be horribly flawed. Excluding himself from the snap would make it into a straight villain, while considering himself equal to the rest would make him into a wannabe hero with very very evil methods. This makes a huge difference in the interpretation of the movie and his character. When to use "If I was" vs. "If I were"? If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English? Where can I find information about upcoming special issues in a field of study? How can I find information about upcoming special issues related to a special field of study? There are good websites for upcoming conferences but I could not find any place to search for special issues. Is there a way to see how the markup of a per-site meta answer is formed? I sometimes see a useful markup feature in a per-site meta answer. However, I cannot edit it to see how one did it, since editing (or suggesting edits) is disabled for users with less than 2k reputation on per-site metas.  Is there a way to see the source code of a per-site meta answer? In TeX, how is computing zero sign written with slanted vertical line on it? `find` with multiple `-name` and `-exec` executes only the last matches of `-name` When I'm using  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt"  it finds all the types of file. But when I add -exec at the end:  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt" -exec sh -c 'echo "$0"' {} \;  it seems it only prints .txt files. What am I doing wrong?  Note: using MINGW (Git Bash) Facebook changed how their API serves profile pictures that are requested with a non-application scope UID. Now because before Graph API 2 all applications shared the original UID, if users like me has joined Stack Exchange websites before  2, rolling out their profile pictures are not shown properly. Facebook suggests to use an access token to query those profile pictures, either an application access token or a user access token. A user access token is not a reliable option at all, because it would only work for users who joined website with Facebook and are currently logged in. Application access tokens, by the way, can be used by creating sort of a proxy that would retrieve a profile picture from Facebook and display it. Yet still it's not perfect. I think the best solution is to communicate with Facebook and ask them to offer an opportunity to convert old Graph API 1 UID's to application scope user IDs. Under the  tag I have seen many questions on earth-616. Are there any other versions of earth as well? How do they differ from each other? I dug a large room to specifications, 3 blocks tall and 16 blocks wide as well as long. I dug it at 10 levels above bedrock, in a location {(-240, 0) -> (-224, 16)} specified by  slime finder app. I am definitely more than 24 blocks away and less than 32 away from the spawn room, as specified by the wiki .  Yet, no slimes. I have been sitting in my location patiently listening for the moist slapping sounds of slime. I have gone in to the room every time I heard a phantom slap but still nothing.  Am I just being dumb somehow or do the minecraft lords just hate me?  If it helps/anyone cares here's my seed: 6405460532872068998