Hello! I have done all of my math homework but I'm so stuck on these couple problems.'

0∫1 [ 1/(1+∛x) ]dx (integral between 0 and 1)

and

∫ [ x²/√(1-x²) ]dx

Thank you!!

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- Jul 13th 2010, 07:21 PMkhch313Evaluating integrals
Hello! I have done all of my math homework but I'm so stuck on these couple problems.'

0∫1 [ 1/(1+∛x) ]dx (integral between 0 and 1)

and

∫ [ x²/√(1-x²) ]dx

Thank you!! - Jul 13th 2010, 07:59 PMProve It
For the second

make the substitution so that .

Then the integral becomes

.

Now remembering that that means and .

So

. - Jul 13th 2010, 08:19 PMkhch313
Thank you!

- Jul 14th 2010, 08:56 AMtom@ballooncalculus
Just in case a picture helps with the other...

http://www.ballooncalculus.org/asy/internal/three.png

... where... (key in spoiler)

__Spoiler__:

Do long division to split up the improper fraction,

__Spoiler__:

________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Jul 14th 2010, 09:52 AMkhch313
- Jul 14th 2010, 05:13 PMProve It
Or without a picture...

.

Let so that and .

So the integral becomes

.

Now substitute your terminals, remembering that if and if .