## anonymous 4 years ago Help with integration. Can someone show me how to do this.

1. anonymous

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

2. anonymous

The inside is squared.

3. anonymous

The e^ix is really bugging me.

4. UnkleRhaukus

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

5. UnkleRhaukus

is that right?

6. anonymous

no no The whole thing inside the integral is squared.

7. anonymous

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

8. anonymous

yes yes.

9. UnkleRhaukus

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

10. anonymous

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

11. inkyvoyd

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

12. 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.

13. inkyvoyd

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

14. 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?

15. anonymous

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

16. anonymous

tried that

17. inkyvoyd

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

18. anonymous

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

19. anonymous

Mathematica is on my dead mac... Ugh

20. 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.

21. anonymous

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

22. anonymous

Change it to polar form maybe?

23. anonymous

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

24. UnkleRhaukus

what do i enter into grapher? @Christbot

25. anonymous

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

26. anonymous

You guys familiar with Euler's formula?

27. anonymous

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

28. anonymous

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

29. anonymous
30. anonymous

That was the original problem I just wrote it wrong.

31. anonymous

Ouch!

32. anonymous

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

33. anonymous

Ouch indeed I hate my life right now. lol

34. anonymous

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

35. anonymous

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

36. anonymous

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

37. anonymous

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

38. anonymous

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

39. anonymous

40. anonymous

TY!!

41. anonymous

Want the last bit or you got it?

42. anonymous

Go it!

43. anonymous

High five!

44. anonymous

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

45. anonymous

No prob! I love a good problem.

46. 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!