Simple Antiderivative

  • Thread starter Icebreaker
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  • #1
Icebreaker
[SOLVED] Simple Antiderivative

How would I compute the antiderivative of

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

It looks familiar, but I can't quite remember how...
 

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  • #2
James R
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Put

[tex]x=\sqrt{2} \sin u[/tex]

and go from there.
 
  • #3
dextercioby
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U can also put the Riemann measure on [itex]\mathbb{R} [/itex] : [itex] dx [/itex]. :wink:

Daniel.
 
  • #4
Icebreaker
Ah yes, of course. Thanks.

Quick follow-up:

[tex]\int\log|\sqrt{1-x^2}+x|[/tex]
 
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  • #5
James R
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I think that integrand is related to an inverse hyperbolic trig function... but I'd have to play around with it to work out which one. Maybe somebody else...
 
  • #6
Icebreaker
Perhaps it simply cannot be expressed algebraically?
 
  • #7
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Icebreaker said:
Perhaps it simply cannot be expressed algebraically?
It cannot be expressed in terms of elementary functions, you are correct.

I love Mathematica :smile:

Alex
 

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