Integral involving square root -need help

  • Thread starter winbacker
  • Start date
  • #1
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Homework Statement



integrate sqrt(1-x^-2/3)^1/2.

Homework Equations





The Attempt at a Solution



The only thing I can think of is u substitution with u = 1 - x^-2/3. Obviously this cannot work because du differs by more than just a constant.

I guess I need to somehow factor this equation but I do not know how. I think I can pull out an x^1/3 or something but I'm not sure. Any help would be appreciated.
 

Answers and Replies

  • #2
659
4
Whenever you see stuff like that in the square root, always think "Trig Substitution"!

Hint: 1-sin(x)^2 = cos(x)^2.
 
  • #3
statdad
Homework Helper
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Do you mean

[tex]
\sqrt{1-x^{-2/3}}
[/tex]

or do you mean (as you've written)
[tex]
\sqrt{(1-x^{-2/3})^{1/2}}
[/tex]
 
  • #4
13
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the first one
 
  • #5
35,428
7,288
Whenever you see stuff like that in the square root, always think "Trig Substitution"!

Hint: 1-sin(x)^2 = cos(x)^2.

I'm not sure that trig substitution is the way to go in this problem. Trig substitution is a viable alternative for integrals that involve
[tex]\sqrt{a^2 + x^2}[/tex]
[tex]\sqrt{a^2 - x^2}[/tex]
[tex]\sqrt{x^2 - a^2}[/tex]

Maybe it can be made to work in the OP's problem, but I don't see it.
 

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