## Romero 3 years ago Help with integration. Can someone show me how to do this.

1. Romero

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

2. Romero

The inside is squared.

3. Romero

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. Romero

no no The whole thing inside the integral is squared.

7. Romero

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

8. Romero

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. Romero

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. Romero

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. christbot

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

16. Romero

tried that

17. inkyvoyd

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

18. christbot

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

19. christbot

Mathematica is on my dead mac... Ugh

20. Romero

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. christbot

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

22. christbot

Change it to polar form maybe?

23. Romero

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. christbot

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

26. christbot

You guys familiar with Euler's formula?

27. Romero

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

28. christbot

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

29. Romero
30. Romero

That was the original problem I just wrote it wrong.

31. christbot

Ouch!

32. Romero

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

33. Romero

Ouch indeed I hate my life right now. lol

34. Romero

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

35. christbot

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

36. christbot

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

37. christbot

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

38. christbot

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

39. christbot

40. Romero

TY!!

41. christbot

Want the last bit or you got it?

42. Romero

Go it!

43. christbot

High five!

44. Romero

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

45. christbot

No prob! I love a good problem.

46. christbot

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!