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.

Printable View

- Oct 15th 2010, 07:52 PMx3bnmIntegration 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. - Oct 15th 2010, 07:58 PMKrizalid
note that $\displaystyle x^3=x^2\cdot x,$ so put $\displaystyle t^2=a^2-x^2.$

- Oct 15th 2010, 08:01 PMmr fantastic
- Oct 15th 2010, 08:06 PM11rdc11
Try the trig sub $\displaystyle x =a\sin{\theta}$

it simplifies to

$\displaystyle a^3\int \sin^3{\theta}d\theta$ - Oct 15th 2010, 08:46 PMx3bnm
Thank you all for your input. Yes at last i solved this integral. I tried both 11rdc11 and Krizalid's way. Both procedures work.

- Oct 16th 2010, 05:20 AMKrizalid