Math Help - integral

1. integral

Hi
I wondered whats the best way to integrate $\int x^2 \sqrt(1-x^2)$

Tried to substitute with $u=1-x^2$ That way i get $x^2 = 1- u$ but I don't know how to continuoe.

Thanks, knut

2. Re: integral

Try $x=\sin(u)$

3. Re: integral

Originally Posted by Knut-o
Hi
I wondered whats the best way to integrate $\int x^2 \sqrt(1-x^2)$

Tried to substitute with $u=1-x^2$ That way i get $x^2 = 1- u$ but I don't know how to continuoe.

Thanks, knut
Where to $dx$ gone?

4. Re: integral

Originally Posted by Also sprach Zarathustra
Where to $dx$ gone?
$\int x^2 \sqrt{1-x^2} dx$

5. Re: integral

Originally Posted by Knut-o
$\int x^2 \sqrt{1-x^2} dx$
If you use the sub I made in my post then $dx = \cos(u) \ du$ and your integral is $\displaystyle \int \sin^2(u)\sqrt{1-\sin^2(u)} \cos(u) du = \int \sin^2(u)\cos^2(u) du$

Does that help?

6. Re: integral

yes! thank you very much