## Romero Group Title Help with integration. Can someone show me how to do this. 2 years ago 2 years ago

1. Romero Group Title

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

2. Romero Group Title

The inside is squared.

3. Romero Group Title

The e^ix is really bugging me.

4. UnkleRhaukus Group Title

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

5. UnkleRhaukus Group Title

is that right?

6. Romero Group Title

no no The whole thing inside the integral is squared.

7. Romero Group Title

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

8. Romero Group Title

yes yes.

9. UnkleRhaukus Group Title

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

10. Romero Group Title

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

11. inkyvoyd Group Title

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

12. inkyvoyd Group Title

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 Group Title

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

14. Romero Group Title

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 Group Title

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

16. Romero Group Title

tried that

17. inkyvoyd Group Title

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

18. christbot Group Title

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

19. christbot Group Title

Mathematica is on my dead mac... Ugh

20. Romero Group Title

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 Group Title

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

22. christbot Group Title

Change it to polar form maybe?

23. Romero Group Title

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

24. UnkleRhaukus Group Title

what do i enter into grapher? @Christbot

25. christbot Group Title

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

26. christbot Group Title

You guys familiar with Euler's formula?

27. Romero Group Title

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

28. christbot Group Title

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

29. Romero Group Title
30. Romero Group Title

That was the original problem I just wrote it wrong.

31. christbot Group Title

Ouch!

32. Romero Group Title

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

33. Romero Group Title

Ouch indeed I hate my life right now. lol

34. Romero Group Title

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

35. christbot Group Title

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

36. christbot Group Title

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

37. christbot Group Title

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

38. christbot Group Title

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

39. christbot Group Title

40. Romero Group Title

TY!!

41. christbot Group Title

Want the last bit or you got it?

42. Romero Group Title

Go it!

43. christbot Group Title

High five!

44. Romero Group Title

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

45. christbot Group Title

No prob! I love a good problem.

46. christbot Group Title

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!