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Simple Antiderivative

by Icebreaker
Tags: antiderivative, simple, solved
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Icebreaker
#1
Oct5-05, 10:31 PM
P: n/a
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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James R
#2
Oct5-05, 10:46 PM
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Put

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

and go from there.
dextercioby
#3
Oct6-05, 03:14 AM
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U can also put the Riemann measure on [itex]\mathbb{R} [/itex] : [itex] dx [/itex].

Daniel.

Icebreaker
#4
Oct6-05, 01:16 PM
P: n/a
Simple Antiderivative

Ah yes, of course. Thanks.

Quick follow-up:

[tex]\int\log|\sqrt{1-x^2}+x|[/tex]
James R
#5
Oct6-05, 09:59 PM
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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...
Icebreaker
#6
Oct6-05, 10:03 PM
P: n/a
Perhaps it simply cannot be expressed algebraically?
amcavoy
#7
Oct6-05, 10:07 PM
P: 666
Quote Quote by Icebreaker
Perhaps it simply cannot be expressed algebraically?
It cannot be expressed in terms of elementary functions, you are correct.

I love Mathematica

Alex


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