Jerk, $j(t)=\dddot x(t)$, acceleration, $a(t)=\ddot x(t)$ and velocity, $v(t)=\dot x(t)$ are derivatives of position, $x(t)$. What is the meaning of the integral of position?  For example, one could write  $$\int x \mathrm{d}t = \int x \frac{\mathrm{d}t}{\mathrm{d}x}\mathrm{d}x = \int x\frac{1}{v} \mathrm{d}x$$  which reminds the equation for .
I know that taking the derivative of position with respect to time defines what we call velocity, but I've never heard of physicist going in the opposite direction with position. Is there any application for the integral of position with respect to time?  Maybe with respect to something else?
Evaluate $$I=\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$$   I try to change it to:$$I=\int_{0}^{1}\frac{(1-x)\log(1-x)}{\log x}dx$$ but I can't do next steps,help me ,thank you very much. Is it possible to edit a layer in QGIS while there is an active query? I am new to Quantum and I am digitizing polygon layers using the editing features. I would like to apply simple queries ('date > 2012/08/01'), however while the query is active I cannot edit the layer. Is this possible? I'm looking for the title of an anthology of children's science fiction stories from the 1950s. The best of the bunch involved a Martian who visited earth, and realized we'd blown ourselves up in a nuclear war and had fallen into savagery. The Martian is a vegetarian who subsists on biscuits made by a machine he brought with him, and communicates by using one of his tentacles to feed messages direction to/from the brain of the person he's talking to.  Inadvertently left behind by his expedition, he initially befriended some children, and eventually managed to rebuild civilization. Presently he dies, but when another expedition comes a generation later, they find the civilization he rebuilt.  there were other stories, but that was the best one.   If I can't find the name of the book it was in, I'd be happy to settle for the name of the author and the title of the story. LaTeXiT is cropping the pdf I am using LaTeXiT (pierre chachatelier, www.chachatelier.fr) - latex equation editor for Powerpoint for mac.  It's producing pdf that appear to be "cropped" on top (see attached) - I've tried already with changing the "margins" option (Preferences>General) but unsuccessfully - don't think that's the problem.   Any hint?   Thanks New Graphics Card Preventing Boot Up Find the sum $\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$ Please help me calculate the following sum     $$\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$$ running script with ". " and with "source " I was wondering if the following two ways of running a bash script are equivalent?  . ./myScript.sh  source myScript.sh  Are they both running the content of the script instead of running the script, i.e. not creating a subshell for running the script? Prepositional Phrase - confused - at or in Let's meet in the morning  or at the morning.  in the afternoon or at the afternoon.  in the night or at the night.  in the park or at the park.  working in the background or at the background. Cardinality of a totally ordered union Let $(X_{\alpha})_{\alpha \in A}, (Y_{\alpha})_{\alpha \in A}$ be families of sets such that for $\{X_{\alpha} \mid \alpha \in A \}$ and $\{Y_{\alpha} \mid \alpha \in A \}$ are totally ordered by inclusion. We have $(X_{\alpha},Y_{\alpha}) \neq (X_{\beta},Y_{\beta})$ for $\alpha \neq \beta$. Suppose that $|X_{\alpha}| \leq |Y_{\alpha}|$ for any $\alpha \in A$. It is true that $|\bigcup_{\alpha} X_{\alpha}| \leq |\bigcup_{\alpha} Y_{\alpha}|$? Python Ctypes - loading dll throws OSError: [WinError 193] %1 is not a valid Win32 application Can you filter out certain SE sites from the hot questions list? Is it possible to filter out Stack Exchange sites from the hot questions list? Name of component on output side cable of a DC power adapter? How do I start with in-camera JPEG settings in Lightroom? I'm a novice shooting in RAW and find that half the time my camera JPEG images come out better than my Lightroom tweaks to RAW files.  So to give myself a better start I'd like to apply the JPEG settings that are applied automatically by the camera to my RAW files in lightroom so that initially my RAW files look exactly like the JPEG files.   How can I do this? Our 21 month old toddler will use the potty when we leave her bottom bare - she has been successfully doing this for a month. Tired of cleaning stinky diapers, we leave her bottom bare when she is home.   She doesn't particularly enjoy wearing diapers, and when we put one on her, she doesn't take the initiative to tell us that she has to use the potty. However, when we have company over, we put a diaper on her.  We are trying to transition her into wearing panties; however, she is very opposed to them. She equates them with pants and doesn't want to wear them. While she is fully capable of dressing herself in pants, she hasn't mastered taking her pants off yet.   How do you introduce underwear to your child? When do people normally introduce underwear to their child? How do I explain the concept of having to take her panties off before using the potty?  We in no way want to discourage her use of the potty, as she seems to really enjoy pooing/peeing outside (she claps for herself whenever she uses the potty). But if she is interested in potty training herself, I do want to show her the concept of an underwear. If every polynomial of degree 2 is reducible then $K$ is algebraically closed? How do I sort a list of dictionaries by a value of the dictionary? I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}] How do we "restore" notepad after crash? I was running NotePad and Chrome when my computer suddenly shuts down.  After reboot, chrome was able to "restore" itself such that I didn't lose any data.  However, how do we "restore" notepad.exe? Are repository lists secure? Is there an HTTPS version? Complicated FOR loop nesting. Having trouble cleaning up legacy code $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$ Let $p(z)= \sum_{k=0}^n a_k z^k$ ,  $a_n \neq 0$ , be a polynomial of degree $n$ such that $|p(z)| \leq M$ for $|z| \leq 1$.  Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$  This was an exam question. Part (a) of this question asked the converse: if $|p(z)| \leq M|z|^n$ and $|z|$ is sufficiently large, then $p(z)$ is a polynomial. This question came straight out of Ahlfors' Complex Analysis, which I solved by showing, using the Cauchy Estimate,  $|p^n (z)|  \leq \frac{n!M|z|^k}{R^n} = 0$ as $R \to \infty$.   I would like to work backwards with this.   May I do this, or similar:   $p(z) = \frac{1}{2\pi i} \int_{c} \frac{f(\zeta)d\zeta}{\zeta-z}$  $\Rightarrow  |p(z)| \leq \frac{2\pi M|z|^n}{1(2\pi)}= M|z|^n$