How do I work this one out? <div class="math">\int_{0}^{2\pi }\frac{dx}{\sqrt{2-\cos x }}</div> I do know it's an elliptic integral but I want to get its value (like pi times something). I tried using Residue theorem but I end up with a clusterfuck of fail and AIDS. Any ideas?

File: 620 KB, 1920x1280, the universe.jpg [View same] [iqdb] [saucenao] [google]

Anonymous Mon Oct 10 16:29:34 2011 No.3881372 [Reply] [Original]

How do I work this one out?

<div class="math">\int_{0}^{2\pi }\frac{dx}{\sqrt{2-\cos x }}</div>

I do know it's an elliptic integral but I want to get its value (like pi times something). I tried using Residue theorem but I end up with a clusterfuck of fail and AIDS. Any ideas?

>>	Anonymous Mon Oct 10 16:37:34 2011 No.3881407 numerically, faggot

>>	Anonymous Mon Oct 10 16:45:34 2011 No.3881452 File: 11 KB, 200x179, okay-meme.jpg [View same] [iqdb] [saucenao] [google] >>3881407 It isnt possible to get a closed value?

>>	Anonymous Mon Oct 10 16:50:34 2011 No.3881477 <div class="math">4\mathit{K}(-2)</div> if you can't series expand it now, kill yourself

Anonymous Mon Oct 10 16:51:34 2011 No.3881480
File: 18 KB, 332x434, cutey_Emma_auyes.jpg [View same] [iqdb] [saucenao] [google]

\int \frac{dx}{\sqrt{2-\cos x }} =
x - x^3/12 + (11 x^5)/480 - (319 x^7)/40320 + O(x^9)

\int_{0}^{2\pi }\frac{dx}{\sqrt{2-\cos x }} =
4.68568033658707943570534352038336732790496620585890268873483368431597\
8439909010478586493754244990090677629187167092704008752807014940993760\
6151965325594479370682533678222818609839188879785713644337818511382509\
8254110988222416038266258572970042044613372586530009674648818218836124\
1611874894672343986447290033937759401968900016134752389290923361947766\
3195576016933116388254103835763105184820268971690341056590828164629261\
6945420372887218595006357599770507381411168342258938082832248456616080\
0724803015345227449569547599060294767618231028938410182179342075639572\
3178582072012883185362692048131938103309827644040699745563116837556336\
3255314616375344206137602997300960001847658788069766381666476883801353\
2232802675962550317795902960901993594347926647636704713675404435784653\
1409879315349752763145052954108782491369788754837706930786672838146583\
8141927755702982612888777910298729624617125913118232912947789633415320\
2827217086681763943410838585264962465999020155061872683717197771905657\
491370714904524691809

>>	Anonymous Mon Oct 10 16:55:34 2011 No.3881502 variable change y=cos(x) ? and then something else i guess

>>	Anonymous Mon Oct 10 16:58:34 2011 No.3881512 Yeah, elliptical integrals. They don't have closed form.

Advanced search
Text to find
Subject [?]Search by post subject. Leave empty for any.
Username [?]Search for user name. Leave empty for any user name.
Tripcode [?]Search for tripcode. Leave empty for any.
Email [?]Search by email. Leave empty for any.
Filename [?]Search by image filename. Leave empty for any.
From Date [?]Enter what date to start searching from. Format is YYYY-MM-DD
To Date [?]Enter what date to start searching until. Format is YYYY-MM-DD
Image hash
Search in	All Posts OPs Only
Deleted posts	Show all posts Show only deleted posts Only show non-deleted posts
Internal posts	Show all posts Show only internal posts Show only archived posts
Order	New posts first Old posts first
Capcode	All Posts Only by Users Only by Mods Only by Admins Only by Developers
Results	Posts Threads
Action	[ Simple ]

/sci/ - Science & Math