Analytical definite integral yields wrong result
Different results for integration using Mathematica and MATLAB
What immigration and customs checks are performed for passengers leaving the U.S.? I wasn't aware of a difference, but a coworker says there is, although he can't back it up. What's the difference if any? Chrome not asking to remember passwords Primary question: A common speaking mistake is to exchange syllables of words, saying "It's trace rhyme!" instead of saying "It's race time!", or pronouncing "kickin' chackatory" instead of "chicken cacciatore." Is there an existing name in poetry, linguistics, or English studies for switching syllables of (quasi-)consecutive words? I am not especially interested in the case when switching syllables results in interpretable homonyms or portmanteaus, like in the first example.  Secondary question: if not, what would you call it?  Tertiary question: is there somewhere a (playful?) taxonomy of fruitful or unfruitful lingual aberrations? Integral vanishes on all intervals implies the function is a.e. zero I am having trouble with the following problem:      $f:\mathbb{R}\to \mathbb{R}$ is a measurable function such that for all $a$:   $$\int_{[0,a]}f\,dm=0.$$   Prove that $f=0$ for $m$ almost every $x$ (here $m$ is the Lebesgue measure).    I have no problem proving this for $f$ non-negative, or under the assumption that $f$ is integrable. But the question only assumes that $f$ is measurable and no more.  My idea was the usual thing; we look at the set of points where $f$ is positive and negative and assume one of these has measure greater than zero. Then I wanted to estimate one of these by an open set, look at the integral on the open set and show that it had to be greater than zero, a contradiction. But a key part of this attack is the assumption of the absolute continuity of the integral, which only holds in the case where $f$ is integrable.  Alternatively, if it were integrable one could simply estimate $f$ by a continuous function, where the result is quite obvious.  Ultimately we are going to show that $f$ is integrable, but it is not clear to me how to show this before showing it is zero a.e. So there must be a simpler way. Does anyone have suggestions? How do I make my rim brakes stop squealing? My rear rim brakes are squeaking loudly. I don't know what the problem is, but I am sure it has nothing to do with rain because it happens all the time even if it is dry.  Anybody have an idea what could be problem and how to solve it? It makes the rear brakes kind of useless, because if I use them I will scare the people or drivers around me. How do I specify a pointer to an overloaded function? Adapt Ubuntu to a high-DPI resolution screen How can I adapt Ubuntu to a high resolution display?  I have a display with 3200x1600px on only 11'' and everything looks really tiny. What happens if you call erase() on a map element while iterating from begin to end? In the following code I loop through a map and test if an element needs to be erased.  Is it safe to erase the element and keep iterating or do I need to collect the keys in another container and do a second loop to call the erase()?  map&lt;string, SerialdMsg::SerialFunction_t&gt;::iterator pm_it; for (pm_it = port_map.begin(); pm_it != port_map.end(); pm_it++) {     if (pm_it-&gt;second == delete_this_id) {         port_map.erase(pm_it-&gt;first);     } }   UPDATE: Of course, I then  which I didn't think would be related but answers my question. I want to prove that the distance between incentre and orthocentre is $$\sqrt{2r^2-4R^2\cos A\cos B\cos C} $$here $r$ is inradius and $R$ is circumradius. I considered $\triangle API$ ($P$ is orthocentre and $I$ is incentre). I could find  $AP=2R\cos A$, $AI=4R\sin\frac{B}{2}\sin\frac{C}{2} $ and $\angle PAI=\angle \frac{B-C}{2}$. So applying cosine rule I got $$PI^2=4R^2+16R^2\sin^2\frac{B}{2}\sin^2\frac{C}{2} -16R^2\cos A\sin\frac{B}{2}\sin\frac{C}{2}\Bigg(\cos\frac{B}{2}\cos\frac{C}{2}+\sin\frac{B}{2}\sin\frac{C}{2}\Bigg)$$ How to proceed form here ? I need rules to drop some malicious Apache connections I drop all traffic on ports except on 80 for my web server.  I have some rules like this on iptables:  iptables -A INPUT -p tcp -m tcp --dport 80 -m string --string "cgi" --algo bm --to 1000 -j DROP   Someone who have more can share? I know always the bad hackers still updating, but some of them always begin with the same code. I need to Drop the connection based on some criteria. Here are some Apache log (I remove ips but each atack come from the same):  Attack 1: This I don't know what are trying to do, but make it 50 times from the same ip  GET / HTTP/1.1  301 224 -   Mozilla/5.0 (X11; Linux i686) AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.152 Safari/537.22 GET / HTTP/1.1  302 3387    -   Mozilla/5.0 (X11; Linux i686) AppleWebKit/537.22 (KHTML, like Gecko) Chrome/25.0.1364.152 Safari/537.22   Attack 2: this try to get information about server only.  GET / HTTP/1.1  301 224 http://myip:80/ Go-http-client/1.1 GET / HTTP/1.1  302 3228    http mywebsite  Go-http-client/1.1 GET /es/ HTTP/1.1   200 40947   https mywebsite Go-http-client/1.1   Attack 3: they try get access to a login page vulnerability  GET /userlogin/login.aspx HTTP/1.1  302 186 -   -   Attack 4: this try to access a cgi at first request, (see my first iptables rule to drop this)  GET /hndUnblock.cgi HTTP/1.0    302 186 -   Wget(linux) GET /tmUnblock.cgi HTTP/1.0 302 186 -   Wget(linux)   I'm very new with server this 4 attacks are from only last 12 hours... Have thousands per week. Switching from MTB to road handlebars Can a deb package contain a PPA dependency and install packages from the PPA? When creating a .deb package I create a file named control that contains some fields:  Package: my-qt-app-name Version: 0.01 Architecture: all Maintainer: my name &lt;my email address&gt; Installed-Size: 2 Depends: some-package-from-ppa Section: extras Priority: optional Homepage: my homepage Description: some description   some-package-from-ppa is not installed on the computer. It can be installed only adding a PPA, running apt-get update and then apt-get install some-package-from-ppa.  Can a control file from a deb package contain a PPA address and install that package when the deb file is installed? Content Assist for JSF2 + CDI (weld) beans + Eclipse Helios Are there any keyboard shortcuts for Windows 10 developer preview's virtual desktops ("Task View")? Trying to install Atom. Unable to start Clangd language server Why are some muggles allowed to know of the magical world? Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$ In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? Ubuntu 16.04 software center doesn't have many apps Given the function   $$ f(x) = \left\{\begin{array}{cc} e^{- \frac{1}{x^2}} &amp; x \neq 0 \\ 0 &amp; x = 0 \end{array}\right. $$  show that $\forall_{n\in \Bbb N} f^{(n)}(0) = 0$.  So I have to show that nth derivative is always equal to zero $0$. Now I guess that it is about finding some dependencies between the previous and next differential but I have yet to notice one. Could you be so kind to help me with that?  Thanks in advance!