Help with integration. Can someone show me how to do this.

- anonymous

Help with integration. Can someone show me how to do this.

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- anonymous

\[\int\limits_0^{2 pi} (\sqrt{1/(3 pi)}+e^{i x}\sqrt{1/(6 pi)} )^2 dx = 2/3 \]

- anonymous

The inside is squared.

- anonymous

The e^ix is really bugging me.

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## More answers

- UnkleRhaukus

\[\int\limits_0^{2\pi}\sqrt{\frac{1}{3\pi}}+e^{ix}\sqrt{\frac{1}{{(6\pi)}^2}}\text d x=\frac 2 3\]

- UnkleRhaukus

is that right?

- anonymous

no no The whole thing inside the integral is squared.

- anonymous

That's why I have a parentheses in the beginning it just doesn't show it that well when i used equations.

- anonymous

yes yes.

- UnkleRhaukus

\[\int\limits_0^{2\pi}\left( {\sqrt{\frac{1}{3\pi}}+e^{ix}\sqrt{\frac{1}{6\pi}}}\right)^2\text d x=\frac 2 3\]

- anonymous

So do I just foil it out and find the integral?

- inkyvoyd

turn e^(ix) into cos x+i sin x.

- inkyvoyd

If 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

Then, replace the g's back with i's. Remember that i^2=-1

- anonymous

If 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)(2pi-0)=2/3 which is the answer but how does that other part cancel out?

- anonymous

Can you copy and paste your integral it into Wolfram Alpha? It will show you how to do it step-by-step

- anonymous

tried that

- inkyvoyd

I would input that into mathematica, but unfortunately my laptop with its installation is being fixed atm

- anonymous

My calc 2 teacher avoided imaginary numbers. So I'm really curious now.

- anonymous

Mathematica is on my dead mac... Ugh

- anonymous

Oh 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.

- anonymous

Anyone have Mac OS X up. Grapher could probably do it.

- anonymous

Change it to polar form maybe?

- anonymous

No the thing is that I was suppose to multiply imaginary function with -imaginary and that just cancels out all the imaginaries.

- UnkleRhaukus

what do i enter into grapher?
@Christbot

- anonymous

Wait, wait never about Grapher... Here http://en.wikipedia.org/wiki/Integration_using_Euler%27s_formula

- anonymous

You guys familiar with Euler's formula?

- anonymous

Yes but I don't need to use it at this point.

- anonymous

Have you tried foiling that giant square and breaking up the integral and placing the e^ix before the integral?

- anonymous

http://www.wolframalpha.com/input/?i=+integrate+from+0+to+2*pi+%28%28%28squareroot%281%2F%283*pi%29%29%2Bsquareroot%281%2F%286*pi%29%29+e%5Eix%29%29*%28%28squareroot%281%2F%283*pi%29%29%2Bsquareroot%281%2F%286*pi%29%29+e%5E-ix%29%29%29

- anonymous

That was the original problem I just wrote it wrong.

- anonymous

Ouch!

- anonymous

I actually got 1 with the addition of some leftover integrals that should cancel out yet I don't really know why.

- anonymous

Ouch indeed I hate my life right now. lol

- anonymous

shouldn't post your phone number on the internet lol and I don't have an iphone. :(

- anonymous

I'm just facebooking myself the input... I'll work to copy and paste, lol

- anonymous

What the hell?! Wolfram won't integrate it?!

- anonymous

Can't we let 1 = trig identity? Wow...

- anonymous

bam I got it as an indefinite integral! Gotta wait for my slow phone, sorry!

- anonymous

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- anonymous

TY!!

- anonymous

Want the last bit or you got it?

- anonymous

Go it!

- anonymous

High five!

- anonymous

*high five*
thanks again!! really helped me out!

- anonymous

No prob! I love a good problem.

- anonymous

Oh 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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