ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: airline on May 08, 2009, 05:43:58 pm

Title: Anti-Diff Help
Post by: airline on May 08, 2009, 05:43:58 pm: Why does...

$\int \frac{1}{\sqrt{x(1-x)}}dx$

equal

$2\sin^{-1}\sqrt{x}+c$
Title: Re: Anti-Diff Help
Post by: dekoyl on May 08, 2009, 05:59:10 pm: Let $u=\sqrt{x}$
$2du=\frac{1}{\sqrt{x}}dx$
Also: $u^2=x$
You will get:
$2\int\frac{1}{\sqrt{1-u^2}}.du$
$=2sin^{-1}(u)+c$
$=2sin^{-1}(\sqrt{x})+c$
Title: Re: Anti-Diff Help
Post by: airline on May 08, 2009, 07:41:32 pm: sorry...but I still don't get it..."du"??
Title: Re: Anti-Diff Help
Post by: TrueTears on May 09, 2009, 01:05:52 am: It's a change of variable.

Subbing in $u = \sqrt{x}$ , we are now trying to integrate with respect to 'u' hence 'du' instead of with respect to 'x' which is 'dx'