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Homework Help: Simple Antiderivative

  1. Oct 5, 2005 #1
    [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...
     
  2. jcsd
  3. Oct 5, 2005 #2

    James R

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    Put

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

    and go from there.
     
  4. Oct 6, 2005 #3

    dextercioby

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    U can also put the Riemann measure on [itex]\mathbb{R} [/itex] : [itex] dx [/itex]. :wink:

    Daniel.
     
  5. Oct 6, 2005 #4
    Ah yes, of course. Thanks.

    Quick follow-up:

    [tex]\int\log|\sqrt{1-x^2}+x|[/tex]
     
    Last edited by a moderator: Oct 6, 2005
  6. Oct 6, 2005 #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...
     
  7. Oct 6, 2005 #6
    Perhaps it simply cannot be expressed algebraically?
     
  8. Oct 6, 2005 #7
    It cannot be expressed in terms of elementary functions, you are correct.

    I love Mathematica :smile:

    Alex
     
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