- #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...

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- Thread starter Icebreaker
- Start date

- #1

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

James R

Science Advisor

Homework Helper

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Put

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

and go from there.

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

and go from there.

- #3

- 13,288

- 1,732

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

Daniel.

Daniel.

- #4

Ah yes, of course. Thanks.

Quick follow-up:

[tex]\int\log|\sqrt{1-x^2}+x|[/tex]

Quick follow-up:

[tex]\int\log|\sqrt{1-x^2}+x|[/tex]

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- #5

James R

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- #6

Perhaps it simply cannot be expressed algebraically?

- #7

amcavoy

- 665

- 0

It cannot be expressed in terms of elementary functions, you are correct.Icebreaker said:Perhaps it simply cannot be expressed algebraically?

I love Mathematica

Alex

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