Integral of $\sqrt{4 - x^2}$?
Integral of $\sqrt{1-x^2}$ using integration by parts
What data type to use for hashed password field and what length? I'm not sure how password hashing works (will be implementing it later), but need to create database schema now.  I'm thinking of limiting passwords to 4-20 characters, but as I understand after encrypting hash string will be of different length.  So, how to store these passwords in the database? Break a previous commit into multiple commits I have a sprite that moves from waypoint to waypoint. It turns to face its velocity vector, but not instantly (there's a rotation speed).  The problem I'm having is, from one direction to another, the sprite will often turn in wild, unnecessary ways instead of appearing like you might expect a car to appear (turn such that the minimum delta in angle occurs).  Right now I'm using the following formula to calculate the rotation float for the current velocity:  MathHelper.PiOver2 + -Math.Atan2(anotherVector.Y - vector.Y, -(anotherVector.X - vector.X));   And then I lerp the current rotation by the new rotation by the rotation speed (10f):  rotation = MathHelper.Lerp(rotation, targetRotation, 10f * (float)gameTime.ElapsedGameTime.TotalSeconds);   But unfortunately, it's causing the sprite to spin in wild directions before reaching the correct angle. Any suggestions? How to extend the text under summation symbol without making extra space What are SPF records, and how do I configure them? Unfortunately, despite having tried to learn regex at least one time a year for as many years as I can remember, I always forget as I use them so infrequently. This year my new year's resolution is to not try and learn regex again - So this year to save me from tears I'll give it to Stack Overflow. (Last Christmas remix).  I want to pass in a string in this format {getThis}, and be returned the string getThis. Could anyone be of assistance in helping to stick to my new year's resolution?    Related questions on Stack Overflow: What was the Historical Precursor for .NET Attributes? What languages or platforms influenced the .NET 1.0 Team to build-in the concept of Attributes from the very start? Was this an Aspect-Oriented thing? Serialization? or something else? I was still in VB6-land at this time, and never used any of the pre-1.0 .NET versions. Homeomorphism is bijective Here is my question:  Is a homeomorphism, that is, a continuos function whose inverse function is also continuous, always bijective? addtocontents not working with certain other packages This is a follow up question on   How do I change the toc dept mid document while using packages (in this case only mathtools).  An example:  \documentclass[a4paper,10pt,oneside]{book}  \usepackage{mathtools}  \begin{document}   \frontmatter             \chapter{hello}  \section{hello}  \subsection{hello}  \subsubsection{hello}   \setcounter{tocdepth}{3}  \tableofcontents   \mainmatter   \chapter{hello}  \section{hello}  \subsection{hello}  \subsubsection{hello}   \chapter{hello}  \section{hello}  \subsection{hello}  \subsubsection{hello}   \appendix   \addtocontents{toc}{\setcounter{tocdepth}{0}}   \chapter{hello}  \section{hello}  \subsection{hello}  \subsubsection{hello}   \chapter{hello}  \section{hello}  \subsection{hello}  \subsubsection{hello}  \end{document}   This example generates an error and very strangely puts an exclamation mark in the ToC as you can see here   however when I comment out the \usepackage{mathtools} it suddenly works again or replacing it with a different package such as \usepackage[T1]{fontenc} also generates no errors.  But this is not limited to just this specific package, certain other packages also introduce the same behavior (I just took this package to keep the example small). Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic? Suppose $A$ is an open subset of $\mathbb{R}^n$ considered as a topological subspace. Suppose $B$ is a another susbet of $\mathbb{R}^n$, and under the induced topology, is homeomorphic to $A$.  If $B$ is closed and bounded, then by the Heine-Borel theorem, $B$ is compact as a topological space so $A$ and $B$ cannot be homeomorhpic, because $A$ is not compact. But if $B$ is not bounded, what can be said about $B$, if any? Must $B$ be open, can it ever be closed (let's leave out the only case of being both open and closed--the entire ambient space $\mathbb{R}^n$), or can it be neither open nor closed? Let $\{f_n\}$ be a sequence of analytic functions on a region $\Omega$ with $|f_n| ≤ 1$ on $\Omega$. Let K be compact and contained in $\Omega$. Suppose $\{f_n\}$ converges at infinitely many points in K. Then is it true or false that $\{f_n\}$ necessarily converges at every point of $\Omega$? What word would describe someone who doesn't generally leave much of an impression on people? When I check for updates, I get a "Failed To Download Repository Information" error.   This is what comes up under details:   W: Failed to fetch gzip:/var/lib/apt/lists/partial/us.archive.ubuntu.com_ubuntu_dists_natty_main_source_Sources  Hash Sum mismatch,  E: Some index files failed to download. They have been ignored, or old ones used instead. Best Place to put Feature Requests? The only place I am aware of is the . How to create a DEB file manually? I want to create a DEB file manually. I would like to just provide a folder which contains data to install, and a script to be executed after installation.  Is this possible? I was just wondering whether the following statement is correct.  Let R be a ring and M a noetherian R module. Then M is finitely generated. PCB opaque coating for anti reverse engineering? Im trying to find a coating for my PCB in order to protect it from reverse engineering. I want it opaque, non-conductive and with a low thermal resistance.  Basically I do not want that someone replicates my circuit easily. I´ve beens searching a lot on coatings but did't find anything that suits to all my requirement. Anyone with an idea? Any tools to generate an XSD schema from an XML instance document? I am looking for a tool which will take an XML instance document and output a corresponding XSD schema.  I certainly recognize that the generated XSD schema will be limited when compared to creating a schema by hand (it probably won't handle optional or repeating elements, or data constraints), but it could at least serve as a quick starting point. Speed of neutrinos Everyone knows it is close to $c$, but how close? What are the recent results? Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns