Evaluate the integral of log(1 + tan x) dx from x=0 to x=pi/4
Let y=tan(x); then x=arctan(y) and dx=dy/(1+y2), the limits are from y=0 to y=1, and the integrand is log(1+y)/(1+y2) dy.
(Henceforth I will assume that by "log" is meant "ln" because that's easier to write; the common interpretation of "log(x)" however is ln(x)/ln(10).)
Now after setting the original integral to S, set up integration by parts, with u=1/(1+y2) and dv=log(1+y) dy; then du=-2y/(1+y2)2, v=(1+y)(log(1+y)-1), and S=ln(2)-int(2y(1+y)(1-log(1+y))/(1+y2)2,y,0,1).
Then moving that huge integral to the other side, int(2y(1+y)/(1+y2)2+(1-y2)log(1+y)/(1+y2)2,y,0,1)=ln(2)...hmmm
At this point I went to Wolfram Alpha and found that it didn't have an expression in terms of real-valued functions of a real variable.
If you liked this run and want to see an idea for a 100% run there is a playlist I've made 2 years ago.
http://www.youtube.com/my_playlists?p=DCEE82033F8D7585
It is slightly out of date because I was discovering new tricks along the way like hyperclimbing and luck manipulating the coins after defeating the boss.
There is a windows version, but IIRC you have to compile it.
I tried loading the solution file and compiling for x64 with VS2010; the code either may not work yet with Win64 or may really need VS2005.
Also there is now a Win32 build of the 1.99.3 beta, and it will work with 64-bit Windows 7 and Vista and x64 XP (but not the old IA64 version, because IA64 has no compatibility with 32-bit x86 apps)
1) The rationals form a set of measure zero, so f(x)=1 on (0,1) almost everywhere, so its Lebesgue integral is 1 (its Riemann integral is undefined; the Lebesgue integral is a proper extension of the concept of "Riemann integral" because if the latter exists, the former also does and is equal to it).
This is already being judged despite there being only 4 votes? I'd watch it and vote but I don't feel like figuring out how to run movie playbacks in VBA.
1. Download VBA-rr
2. Download "Shining Soul II (U)" ROM
3. Download the submission
4. Open all the ZIP, RAR, 7z, etc. files; you should have a .exe, a .vba, and a .vbm somewhere.
5. Launch VBA-rr (no installation required), Open the ROM, then go to Tools>Movie>Play Movie and choose the submission file.
technically it's an ISO because it's an image of an ISO 9660 file system; a ROM is an image of the contents of a chip containing ROM (Read-Only Memory)
He went on a mission from God and lost interest in maintaining the site, so he offered to let some other people take care of the site, and then adelikat and Nach stepped up to take it off his hands.
Wow, and using a non-existent emulator to do it too! :) Kinda boring, but not enough to kill the entertainment of the glitchiness. Broken indeed. Yes vote.
Mr. Kelly R. Flewin
I saw some of those back when I used that very site to download Snes9x 1.52
but I don't know enough about the relationship between the changes and the addition of re-recording functionality
That's weird, because it does exist in the original Windows version of Snes9x 1.52; I originally said "the problem is that Snes9x-rr doesn't exist for Mac" but changed it when I remembered that regular Snes9x does exist for Mac, and the regular Windows version does have that menu.
Maybe the place to customize hotkeys is different on the Mac, kinda like how "Tools>Options" in most Windows apps becomes "Edit>Preferences" on Linux apps or "(app name)>Preferences" on the Mac
