# Integration problem with impossible integral

• October 15th 2010, 07:52 PM
x3bnm
Integration problem with impossible integral
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?
$
\int_0^a \frac{x^3}{\sqrt{a^2-x^2}} dx
$

Thanks.
• October 15th 2010, 07:58 PM
Krizalid
note that $x^3=x^2\cdot x,$ so put $t^2=a^2-x^2.$
• October 15th 2010, 08:01 PM
mr fantastic
Quote:

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 ....! (Evilgrin) 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 ....)
• October 15th 2010, 08:06 PM
11rdc11
Try the trig sub $x =a\sin{\theta}$

it simplifies to

$a^3\int \sin^3{\theta}d\theta$
• October 15th 2010, 08:46 PM
x3bnm
Thank you all for your input. Yes at last i solved this integral. I tried both 11rdc11 and Krizalid's way. Both procedures work.
• October 16th 2010, 05:20 AM
Krizalid
Quote:

Originally Posted by mr fantastic
Why bother .... The OP said the integral was impossible ....! (Evilgrin) 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. :D