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Romero
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_0^{2 pi} (\sqrt{1/(3 pi)}+e^{i x}\sqrt{1/(6 pi)} )^2 dx = 2/3 \]

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1The e^ix is really bugging me.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_0^{2\pi}\sqrt{\frac{1}{3\pi}}+e^{ix}\sqrt{\frac{1}{{(6\pi)}^2}}\text d x=\frac 2 3\]

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1no no The whole thing inside the integral is squared.

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1That's why I have a parentheses in the beginning it just doesn't show it that well when i used equations.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_0^{2\pi}\left( {\sqrt{\frac{1}{3\pi}}+e^{ix}\sqrt{\frac{1}{6\pi}}}\right)^2\text d x=\frac 2 3\]

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1So do I just foil it out and find the integral?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0turn e^(ix) into cos x+i sin x.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0If it really bothers you that much. I would just treat i as a constnat. Replace i with g and just integrate it like a constant.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Then, replace the g's back with i's. Remember that i^2=1

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1If I carry out the foil I know that I can split it into three different integral with the first one being integrating 1/3pi If I do that I can simply take out 1/3pi since it's a constant and I get (1/3pi)(2pi0)=2/3 which is the answer but how does that other part cancel out?

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Can you copy and paste your integral it into Wolfram Alpha? It will show you how to do it stepbystep

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I would input that into mathematica, but unfortunately my laptop with its installation is being fixed atm

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1My calc 2 teacher avoided imaginary numbers. So I'm really curious now.

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Mathematica is on my dead mac... Ugh

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1Oh I think I know what I did wrong. I was suppose to multiply the inside function with it's complex conjugate so it cancels out all imaginar values.

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Anyone have Mac OS X up. Grapher could probably do it.

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Change it to polar form maybe?

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1No the thing is that I was suppose to multiply imaginary function with imaginary and that just cancels out all the imaginaries.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0what do i enter into grapher? @Christbot

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Wait, wait never about Grapher... Here http://en.wikipedia.org/wiki/Integration_using_Euler%27s_formula

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1You guys familiar with Euler's formula?

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1Yes but I don't need to use it at this point.

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Have you tried foiling that giant square and breaking up the integral and placing the e^ix before the integral?

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1That was the original problem I just wrote it wrong.

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1I actually got 1 with the addition of some leftover integrals that should cancel out yet I don't really know why.

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1Ouch indeed I hate my life right now. lol

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1shouldn't post your phone number on the internet lol and I don't have an iphone. :(

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1I'm just facebooking myself the input... I'll work to copy and paste, lol

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1What the hell?! Wolfram won't integrate it?!

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Can't we let 1 = trig identity? Wow...

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1bam I got it as an indefinite integral! Gotta wait for my slow phone, sorry!

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Want the last bit or you got it?

Romero
 2 years ago
Best ResponseYou've already chosen the best response.1*high five* thanks again!! really helped me out!

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1No prob! I love a good problem.

christbot
 2 years ago
Best ResponseYou've already chosen the best response.1Oh the web version works for free. Yeah, sometime you just gotta tinker with the input. I'm deleting the image links, but here is my mathy blog, FWIW http://mathstem.blogspot.com/ I'll delete my cell# too, lol!
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