Integration problem with impossible integral

**x3bnm** · October 15th 2010, 07:52 PM

I found an integration problem for which I can't find the answer from the top my head. Is there an easy way to integrate the following integral?
$<br /> \int_0^a \frac{x^3}{\sqrt{a^2-x^2}} dx<br />$

Thanks.

**Krizalid** · October 15th 2010, 07:58 PM

note that $x^3=x^2\cdot x,$ so put $t^2=a^2-x^2.$

**mr fantastic** · October 15th 2010, 08:01 PM

Originally Posted by Krizalid

note that $x^3=x^2\cdot x,$ so put $t^2=a^2-x^2.$

Why bother .... The OP said the integral was impossible ....!

I don't know why anyone would want to try and do an impossible integral. (Now, if it was an integral that was difficult for the OP, then that would be a different matter ....)

**11rdc11** · October 15th 2010, 08:06 PM

Try the trig sub $x =a\sin{\theta}$

it simplifies to

$a^3\int \sin^3{\theta}d\theta$

**x3bnm** · October 15th 2010, 08:46 PM

Thank you all for your input. Yes at last i solved this integral. I tried both 11rdc11 and Krizalid's way. Both procedures work.

**Krizalid** · October 16th 2010, 05:20 AM

Originally Posted by mr fantastic

Why bother .... The OP said the integral was impossible ....!

I don't know why anyone would want to try and do an impossible integral. (Now, if it was an integral that was difficult for the OP, then that would be a different matter ....)

ahaha, no matter, actually i just read "integration" and then decided to post.

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