• Support PF! Buy your school textbooks, materials and every day products Here!

Trigonometric integral

  • Thread starter darioe
  • Start date
  • #1
5
0

Homework Statement



Integrate at interval [0,T] (T and k are given real numbers) the

2. Relevant equation

[tex]_{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp[/tex]

The Attempt at a Solution



[tex]\ Using\ substitution\ u\ =\ tan(p/2),\ results\ as\ :\ p\ =\ 2*arctan(u)\ \ ;\ \ dp\ =\ \frac{2}{1+u^2}\ du\ ;\ [/tex]

[tex]sin(p)\ =\ \frac{2*u}{1+u^2} ;\ cos(p)\ =\ \frac{1-u^2}{1+u^2} ;\ [/tex]

[tex]_{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp \ \ =\ _{0}^{2*arctan(T)}\int \frac{2*u*2}{(1+u^2)\ *\ \sqrt{k+2*arctan(u)}\ *\ (1+u^2)}\ du[/tex]

[tex]\ ¿\ Could\ someone\ get\ a\ better\ result\ ?[/tex]

(maybe with the substitution u = 2* sin(p) )


...
 

Answers and Replies

  • #2
1,838
7
See e.g. 16 http://mathworld.wolfram.com/FresnelIntegrals.html" [Broken]
 
Last edited by a moderator:
  • #3
5
0
Should be:

[tex]
_{0}^{T}\int \frac{sin(p)}{\sqrt{k+p}}\ dp \ \ =\ _{0}^{tan(T/2)}\int \frac{2*u*2}{(1+u^2)\ *\ \sqrt{k+2*arctan(u)}\ *\ (1+u^2)}\ du
[/tex]

but it looks like I could have to know about Fresnel Integrals. Thank you for the help.


.
 

Related Threads on Trigonometric integral

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
713
  • Last Post
Replies
2
Views
918
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
2K
Top