# Thread: Integration problem with impossible integral

1. ## 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?
$\displaystyle \int_0^a \frac{x^3}{\sqrt{a^2-x^2}} dx$

Thanks.

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

3. Originally Posted by Krizalid
note that $\displaystyle x^3=x^2\cdot x,$ so put $\displaystyle t^2=a^2-x^2.$
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 ....)

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

it simplifies to

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

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

6. 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.