Question

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

Answer 1

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

Answer 2

The inside is squared.

Answer 3

The e^ix is really bugging me.

Answer 4

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

Answer 5

is that right?

Answer 6

no no The whole thing inside the integral is squared.

Answer 7

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

Answer 8

yes yes.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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.

Answer 13

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

Answer 14

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?

Answer 15

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

Answer 16

tried that

Answer 17

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

Answer 18

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

Answer 19

Mathematica is on my dead mac... Ugh

Answer 20

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.

Answer 21

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

Answer 22

Change it to polar form maybe?

Answer 23

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

Answer 24

what do i enter into grapher?
@Christbot

Answer 25

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

Answer 26

You guys familiar with Euler's formula?

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

That was the original problem I just wrote it wrong.

Answer 31

Ouch!

Answer 32

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

Answer 33

Ouch indeed I hate my life right now. lol

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

TY!!

Answer 40

Want the last bit or you got it?

Answer 41

Go it!

Answer 42

High five!

Answer 43

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

Answer 44

No prob! I love a good problem.

Answer 45

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!