$\int_0^1\bigl( f(x)+f^{-1}(x )\bigr)\>dx=1$
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
class variable vs instance variable --Python How to assign same Data to multiple object copies What does “would not have been possible had I remained” mean? What does this mean?      I am sure this would not have been possible had I remained a typical Anglophone North American.   I have never heard that before and I really find it strange.  I deduce that it means      I am sure this would not have been possible if I kept remaining Anglophone North American.   But I might be wrong in this. How would one write object-oriented code in C? Visual Flow: How to set Date field to Null / Blank? Apache error "Could not reliably determine the server's fully qualified domain name" No secondary button (right click) on touchpad I'm experiencing a serious problem with the new Ubuntu 18.04:  System Dell XPS 13 with a freshly installed Ubuntu 18.04 LTS.  Problem description The touchpad provides only primary button (single click and double click), but no secondary button. In particular, when using the "test Your Settings" option in Settings -> Devices -> Mouse &amp; Touchpad, any click on the touchpad is signaled as primary button, no matter where I click (left or right side of the touchpad). This remains the case even after I change the Primary Button from Left to Right (in Settings -> Devices -> Mouse &amp; Touchpad -> General).  In comparison, an external mouse connected to my laptop (via usb) works fine: it provides both primary and secondary buttons with sides corresponding to the choice of Primary Button (in Settings -> Devices -> Mouse &amp; Touchpad -> General).  This may be related to   Any ideas?  Update: Meanwhile, I found out that in addition to the solution proposed by EntropyWins, one can also control this touchpad behavior via the Tweaks tool (a.k.a. gnome-tweaks) under Keyboard &amp; Mouse -> Touchpad -> Mouse Click Emulation. In any case, as EntropyWins explains in his answer, this is not a bug. 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? Symmetric powers of modules Force pagebreak after every sentence/paragraph Is there a way to force a pagebreak after every sentence or paragraph?  This may seem like an odd thing to do, but for catching typos and just general editing I find it much easier to look at a sentence or paragraph in isolation so that I am not tempted to skip ahead.  Currently, I just zoom in so I can only see a few word at a time, but this is not a perfect solution. What is the value of $\sum\limits_{i=1}^\infty\frac{1}{p_{p_i}}$ where $p_{i}$ is the $i$th prime? What is the value of $\sum\limits_{i=1}^\infty\dfrac{1}{p_{p_i}}$ where $p_n$ is the nth prime (and so $p_{p_n}$ is the $k$th prime, where $k$ is the $n$th prime) ?  Thus $\frac{1}{3}+\frac{1}{5}+\frac{1}{11}+...=$ ??  How do I efficiently decide if $\sum_{i=1}^\infty\dfrac{1}{p_{p_i}}\gt1$ is true without using a computer ?  I assume this infinite sum is an irrational number. Has this already been proven ? UIToolbar tint on iOS 4 What is the function of the RNA primer in DNA replication? no wifi in Ubuntu 15.04 Windows Unable to Delete ._. File I currently have a file on the root of my external hard drive simply named ._., which I am guessing was added to my hard drive after using it on my MacBook a while ago.  I'm trying to delete this file on my Windows 10 machine; however Windows keeps claiming the file cannot be found.    I also tried deleting the file through an elevated command prompt; however the same message is returned.    Is there any way I can delete this file from my hard drive through Windows? Moving set of polygons in ArcGIS Pro? How do I find out which process is eating up my bandwidth? I think I'm being the victim of a bug here. Sometimes while I'm working (I still don't know why), my network traffic goes up to 200 KB/s and stays that way, even tough I'm not doing anything internet-related.   This sometimes happens to me with the CPU usage. When it does, I just run a top command to find out which process is responsible and then kill it. Problem is: I have no way of knowing which process is responsible for my high network usage. Both the resource monitor and the top command only tell me my total network usage, neither of them tells me process specific network info.  I've found questions here about monitoring total bandwidth usage, but, as I mentioned, that's not what I need. Is there another command I can use to find out which process is getting out of hand?  The command iftop gives results that disagree entirely with the information reported by System Monitor. While the latter claims there's high network traffic, the former claims there's barely 1 KB/s.  I've already tried killing all the obvious ones (Firefox, update-manager, Pidgin, etc) with no luck. So far, restarting the machine is the only way I found of getting rid of the issue. What are the pros and cons of the leading Java HTML parsers? To hyphenate or not? tikz package causing error in IEEE access template I have been trying for a while to load the tikz package to the IEEE ACCESS template. Whenever I use the command \usepackage{tikz}, I am getting the error   /usr/local/texlive/2017/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex, line 33 Missing number, treated as zero.   It was working fine with the IEEEtran template and I was able to draw my circuit diagrams in that.   Anyone has any idea how to solve this issue?