I am interested in showing  that: $$\int_0^{\pi /2}\frac{dx}{\sqrt{\cos{x}}}=\int_0^{\pi /2}\frac{dx}{\sqrt{\sin{x}}}=\frac{\Gamma^2(\frac{1}{4})}{2\sqrt{2 \pi}}$$ I've come across this equality without anything else, would you please help me what I should do?
Compute the Riemann integral  $$\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$$  It seems very difficult, I don't know how to go ahead.  Thank you very much for your help!
Is there evidence to suggest that Supreme Leader Snoke is Darth Plagueis? In Episode III,  explains to Anakin the power of the Dark Side to save people from death. He mentions  - the Sith who discovered this. Sidious then claims he died, which seems odd, given that kind of power.   Then in Episode VII (The Force Awakens) we find a Sith Lord who has appeared from no where. There seems to be two loose ends that fit nicely together.   My question is: Is there evidence to suggest that Supreme Leader Snoke is Darth Plagueis? How can I check if my (unlocked) phone will work with a particular country's SIM cards, for 3G and calls? I've used my phone overseas with local SIM cards a lot, but recently had a surprising experience where one local SIM card simply wouldn't work with my phone but did work first time on my partner's, even though both were similar (unlocked Android phones) and another SIM card from a different local provider did work. Looking into it, it looks like there are various different standards around, but it all gets very technical very quickly.  Is there any simple way of looking up which SIM cards in a particular country will work with a particular model of phone, for calls, texts and internet access? Prove $n!>2^n$ for $n\geq4$ using induction. I just want to know if my proof to this question is correct. First, I proved it was true for $n = 4$. $$4!&gt;2^4$$ $$24&gt;16$$ Then, I assumed that it was true for $n=k$. $$k!&gt;2^k$$ Afterwards, I tried to prove it for $n=k+1$. $$(k+1)!&gt;2^{k+1}$$ $$(k+1)k!&gt;(2)(2^k)$$ Since $k!&gt;2^k$, am I allowed to simply do $$(k+1)(2^k)&gt;(2)(2^k)$$ $$(k+1)&gt;2$$ and this is true for all $k\geq3$. Would the last two steps be illegal because I only assumed that $k!&gt;2^k$ is true? How to create a batch job, numbering images (writing text on them) from 1 to 100 in Photoshop? Looking to create a 100 images that would have their appropriate numbers written on them.  Since I`ll be most likely making changes to the template in the future I figured it would be better to automate it somehow.  Is there a simple solution to this problem? Buying from AliExpress I've notice that the business to business site AliBaba and it's more consumer friendly AliExpress website have a number of bike components for sale. They tend to be complete component groupsets and the like but are some quite reasonable deals, especially if you are building a bike from scratch.  I've used AliExpress before to purchase electronic components, which have been good quality and are what they say on the tin.   Has anyone used AliExpress to buy bike components and have they had any trouble? (quality, counterfeit etc.)  One benefit is that your money is held in escrow until you receive the item and aprove the payment so some safety. I have installed the developer preview for Yosemite.  Huge mistake. Everything in my workspace is broken.  I don't have any sort of backup image. I was wondering if I could re-download Mavericks and run the installer - would that effectively downgrade me back to Mavericks? What is the acceptable similarity in a mathematics PhD dissertation when checking by Turnitin? I have checked the originality of my PhD thesis in mathematics using . The similarity was 31%. Is this percentage acceptable by most committees? How to filter features in a layer? I am trying to display certain features in a shapefile-based layer using QGIS. I have found the subset function in the properties panel, which does exactly what i want, but is too tedious given that I have to manually sift through a large number of features. Is there a quicker way to do this?  I am using both shapefiles and postGIS best,  dietmar Prevent mail being marked as spam This is a  about avoiding outgoing mail being classified as spam.   Also related:                    I'm wondering how to prevent my emails from my site being marked as spam? I'm using sendmail.  I'm trying to send emails through my ruby-on-rails application. The mails are all written in swedish (if that does make a difference?). I don't know why they keep getting marked as spam.  Are there any things that I can do to minimize the risk? How to turn off the iOS-style character picker menu Interpreting exp(B) in multinomial logistic regression This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model?  1) is it 6.012-1.0 = 5.012 = 5012% increase in risk?  or  2) 6.012/(1+6.012) = 0.857 = 85.7% increase in risk?  In case both alternatives are incorrect, can someone please mention the correct way?  Ive searched many resources on the internet and I get to these two alternatives, and I am not entirely sure which one is correct. Skew symmetry of indices in cocycles of Cech cohomology In Cech cohomology, the coboundary operator $$\delta:C^p(\underline U, \mathcal F)\to C^{p+1}(\underline U, \mathcal F) $$ is defined by the formula $$ (\delta \sigma)_{i_0,\dots, i_{p+1}} = \sum_{j=0}^{p+1}(-1)^j \sigma_{i_0,\dots, \hat {i_j},\dots i_{p+1}}{\Huge_|}_{U_{i_0}\cap\dots\cap U_{i_{p+1}}}. $$ In the book by Griffiths and Harris, the authors claim that $\delta\sigma=0$ implies the skew-symmetry condition $$ \sigma_{i_0,\dots,i_p} = -\sigma_{i_0,\dots, i_{q-1},i_{q+1},i_q,i_{q+2},\dots,i_p}. $$ How can I see this?  EDIT: Or is it possible that the skew symmetry is merely an assumption for all cochains? Ubuntu installation is slow, why? I am currently installing Ubuntu 12.04.3. Everything was going fine until I came across this...     Installing System   It is sssooooooo close to being finished! Like 1/6 of the way there! I just wanted to know if this is normal or if something is wrong. I'm installing it through a flash drive if that helps   Also,what will happen if I press the skip button that pops up when I click Installing System? My girlfriend forgot the password for her MacBook (don't ask), so I reset it using the Utilities.  But as you may be aware, this doesn't reset the Keychain password. Her MacBook is now virtually unusable due to Keychain demands continuously provoking a request for the Keychain password.  There are lots of other people asking this around the web and they're usually pointed towards this , which doesn't apply in our situation because the support advice involves entering the old password.  We don't know the old password.  Is it possible to reset Keychain without knowing the old password? We're not bothered about what's in there and what will be lost, we just want the continuous password prompts to go away. Let $G$ be a finite group. For each positive integer $m$, if $x^{m}=e$ has at most $m$ solutions in $G$, $G$ is cyclic.   What I have thought is that $n=\sum_{d\mid n}\phi(d)$ can be used to solve this and showing that $|G|$ order element in $G$ exists is enough. What exactly is "pressure", and what's its relation to force? List manipulation: position & max value combination Let $R$ be a finite ring with unity. Prove that every nonzero element of $R$ is either a unit or a zero-divisor. Minimum safe spacing between lava and flamable materials? It seems that containing lava in solid glass, stone and iron blocks may not be sufficient to prevent wool from burning, even if the lava is completely encased.         After some delay, it seems that fire will jump onto the wool above the iron.   Are solid blocks more effective than airspace, or not? If so, Does it matter whether the corner block is filled in? What are the exact rules on distance that I need, and how can I prevent flammable blocks from being eliminated by nearby lava? Bonus: Does a flowing lava block behave differently than a lava source block when it comes to fire creation? Sharepoint 2010 - Deploy webpart as Feature scope = web