Trigonometric Integral excersice

  • Thread starter alba_ei
  • Start date
  • #1
38
1

Homework Statement


Integral of [tex] \int \sin^{11/3}\alpha\, d\alpha [/tex]


Homework Equations


[tex]\sin^2\alpha = 1 - cos^2\alpha [/tex]


The Attempt at a Solution


[tex]\int (\sin^2\alpha)^{4/3}\sin\alpha \, d\alpha[/tex]

[tex]\int (1-cos^2\alpha)^{4/3}\sin\alpha \, d\alpha[/tex]

[tex]u = \cos\alphad[/tex]
[tex]du = \sin\alpha\, d\alpha [/tex]

[tex]\int (1-u^2)^{4/3} du [/tex]
i dont know what else to do. any hints or tips?
 
Last edited:

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
13,024
579
Interesting integral. Mathematica returns an answer involving the Gauss hypergeometric function [itex] _{2}F_{1} [/itex]
 
  • #3
682
1
the integral seems pretty hopeless to evaluate due to the cubic root... are there bounds to the integral? that could potentially simply things a whole lot.
 
  • #4
38
1
the integral seems pretty hopeless to evaluate due to the cubic root... are there bounds to the integral? that could potentially simply things a whole lot.
It doesnt have upper or lower limits im just looking for the antiderivate
 

Related Threads on Trigonometric Integral excersice

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
758
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
954
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
2K
Top