[SOLVED] Simple Antiderivative


by Icebreaker
Tags: antiderivative, simple, solved
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...
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
James R
James R is offline
#2
Oct5-05, 10:46 PM
Sci Advisor
HW Helper
PF Gold
P: 562
Put

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

and go from there.
dextercioby
dextercioby is offline
#3
Oct6-05, 03:14 AM
Sci Advisor
HW Helper
P: 11,863
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

[SOLVED] Simple Antiderivative


Ah yes, of course. Thanks.

Quick follow-up:

[tex]\int\log|\sqrt{1-x^2}+x|[/tex]
James R
James R is offline
#5
Oct6-05, 09:59 PM
Sci Advisor
HW Helper
PF Gold
P: 562
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
amcavoy is offline
#7
Oct6-05, 10:07 PM
P: 669
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


Register to reply

Related Discussions
[SOLVED] antiderivative Calculus & Beyond Homework 6
[SOLVED] Finding an Antiderivative in an Annulus Calculus & Beyond Homework 19
[SOLVED] Antiderivative of (sin x)^3/2 Calculus & Beyond Homework 2
[SOLVED] i think this should be simple, but i need help! Precalculus Mathematics Homework 10
simple antiderivative Calculus & Beyond Homework 6