Calculating $\int_{0}^{\infty} x^{a-1} \cos(x) \ \mathrm dx = \Gamma(a) \cos (\pi a/2)$
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
Why is there a mismatch between size reported by LVM and the size reported by df -h? I'm new to LVM and have been very confused by this:  I am transfering a large file to a partition that I thought had about 1.5 terabytes of space on it.  Near the end of the transfer, rsync exits with an error claiming that the partition is full.  I investigate and find the following:  $ sudo lvm lvs   LV        VG     Attr   LSize   Origin Snap%  Move Log Copy%  Convert   home      system -wi-ao  97.66G                                         log       system -wi-ao  48.81G                                         log.audit system -wi-ao   9.75G                                         root      system -wi-ao 341.59G                                         swap      system -wi-ao   4.88G                                         temp      system -wi-ao  97.66G                                         var       system -wi-ao   1.46T     This seems to imply that /var (the partition that I'm transfering to, has the amount of storage I expect.  However, then I see:  $ sudo df -h Filesystem            Size  Used Avail Use% Mounted on /dev/mapper/system-root                       331G  1.3G  313G   1% / /dev/mapper/system-temp                        95G  188M   90G   1% /tmp /dev/mapper/system-var                        95G   90G     0 100% /var /dev/mapper/system-home                        95G  188M   90G   1% /home /dev/mapper/system-log                        48G  264M   45G   1% /var/log /dev/mapper/system-log.audit                       9.5G  340M  8.7G   4% /var/log/audit /dev/sda1              99M   25M   70M  26% /boot tmpfs                 8.0G     0  8.0G   0% /dev/shm   I'm guessing this has something to do with the volume being resized at some point.  While I have reliable backups, I'd rather not interrupt services for the time it will take to get the backup and restore.  Thus, is there anyway to make the filesystem seen by the OS match the space available according to lvm without losing data? Well, I have come to understand persons with the following traits will be usually be Sorted to Slytherin   Resourcefulness  Cunning Ambition Leadership Qualities Self-Preservation Determination  Cleverness Fraternity  Power   On which trait(s) was Snape Sorted into Slytherin?  One more point: Lily Evans was Sorted before Snape, and when she was placed in Gryffindor, obviously Snape wanted to be in Gryffindor too, because Lily is his only friend.   So why is he Sorted into Slytherin? Is there a stronger reason for the Sorting Hat to override his preference and Sort him into Slytherin? I am a bit confused. When can we omit the preposition on before weekdays? (Monday, Tuesday etc.) Sometimes I read weekdays without the preposition on. If the preposition is left out, does it work the same way, or does it change the meaning?  Example without the preposition     The UGC issued the public notice Monday after its two previous orders   in this regard were overlooked by the DU.   Example with the preposition     The commission on Monday also issued a public notice against the FYUP   in all leading newspapers for parents and students. Is it possible to run Snow Leopard on a LATE 2011 MacBook Pro? I want to buy a new MacBook Pro, from Apple. However I want to run Snow Leopard instead of Lion.  I did some Google searches and found a few success stories of people who got SL to run on their early-2011 MBPs. I didn't find much of any experiences of people doing the same on a late-2011 MBP though, so I'm wondering (and really hoping!) if it's possible? Show that f(x) = inf{g(x1)+h(x2)} is convex subject to x1+x2=x and where g(.) and h(.) are convex functions.  Can I just go about this by using the regular definition of a convex function or which properties should I use? I know that the sum of convex functions is convex, but the infimum part confuses me. Thank you Propose Newbie-Overflow site or section What is the closed form of $\int e^{x^2} \, dx$? How can I do a closed form expansion of $\int e^{x^2} \, dx$? Please be specific as to which method I must use. When I'm not exploring fresh caves or lands in minecraft, I'm busy trying to find deposits of diamond, gold and iron deep in the earth. So far I've just been digging around just above bedrock on a whim to look for these rare minerals but I've started thinking that I should be taking a more controlled, efficient approach to mining.  What is the optimal mining strategy that yields the most rare minerals while minimizing blocks removed and time spent digging and traveling?  Edit: The existing answers are great for mining, but no one has addressed travel time to and from the mine which is usually ~60 blocks downward and incredibly tedious. Solutions? Can sudo be reinstalled after being removed? Creating checkbox parameter in Python script tool for ArcGIS Desktop? I am working on creating an ArcGIS tool from a Python script I am writing.  I am wondering if it is possible to have a checkbox parameter.    I want to have a parameter where the user selects a feature class, then from the feature class the user will choose the field for the upper most layer in their model, then I want the user to be able to choose what layers they want the script to run on with a checkbox structure derived from the upper most layer field.    Is this possible with python, and ArcGIS Desktop? past simple or present perfect Partition 256 GB SSD for dual Boot, Windows 10 + Ubuntu 19.04 I plan on installing Ubuntu 19.04 and give it 100 GB of my 256 GB SSD space and leave the rest for Windows as I would primarily be using Ubuntu.     A. Now, as I plan to install a lot of applications in Ubuntu, should I give more space to the / partition than the home partition? (Or maybe even drop the /home altogether?).    B. I have another 128 GB SD card for files like photos, audio and video files. Please suggest me the optimal partitioning for the use case.    C. Also, I have 8 GB of RAM so what should be the optimal swap partition size?    D. How would the distribution be if I choose "install Ubuntu alongside Windows" option? In a letter-class document that had no previous errors I am suddenly getting the error message:  "There's no line here to end" \opening{text}   I've used this file many times and today it starts giving this error. How do I troubleshoot this? How did Vader saving Luke turn him to the good side? Couldn't Vader save his son and continue being a Sith Lord? Couldn't he have let Luke go and basically become the Emperor and have the Galaxy to himself? I don't think killing the Emperor to save your son will automatically convert you to the light side. Enlighten me. GCD of two numbers divided by their greatest common divisor is 1 I have a simple 2-column layout with a footer that clears both the right and left div in my markup.  My problem is that I can't get the footer to stay at the bottom of the page in all browsers.  It works if the content pushes the footer down, but that's not always the case. Microsoft Office alternative for Windows? Is there something similar to Office for Windows but free? I am student living on a budget, Office is not an option at the moment. I don't know how to prove this example. Let $y(t):\mathbb{R}^+\to \mathbb{R}$ be a nonincreasing function. Assume that there is a constant $A&gt;0$ such that \begin{equation} \int_{s}^{+\infty}y(t)dt \leq Ay(s), \quad 0\leq s&lt;+\infty \end{equation} Then $y(t)\leq y(0)e^{1-\frac{t}{A}}$, for all $t&gt;0$. How do you check if a selector matches something in jQuery? In Mootools, I'd just run if ($('target')) { ... }.  Does if ($('#target')) { ... } in jQuery work the same way? I have a list of tuples like this:  [ ('a', 1), ('a', 2), ('a', 3), ('b', 1), ('b', 2), ('c', 1), ]   I want to iterate through this keying by the first item, so, for example, I could print something like this:  a 1 2 3 b 1 2 c 1   How would I go about doing this without keeping an item to track whether the first item is the same as I loop around the tuples? This feels rather messy (plus I have to sort the list to start with)...