Anti-Diff Help

We have moved!

We want to extend a heartfelt thanks to everyone who has made the original ATAR Notes forum such a helpful, warm and welcoming place. Your contributions are appreciated and we will be leaving the forum in archive mode for posterity.

Please visit our new website and discussion area.

Welcome, Guest. Please login or register.

Print

Pages: [1] Go Down

Author Topic: Anti-Diff Help (Read 895 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

airline

Victorian
Trailblazer
Posts: 49
Respect: +1

Anti-Diff Help

« on: May 08, 2009, 05:43:58 pm »

0

Why does...

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

equal

$2\sin^{-1}\sqrt{x}+c$

Logged

dekoyl

Victorian
ATAR Notes Superstar
Posts: 2152
Respect: +18

Re: Anti-Diff Help

« Reply #1 on: May 08, 2009, 05:59:10 pm »

0

Let $u=\sqrt{x}$
$2du=\frac{1}{\sqrt{x}}dx$
Also: $u^2=x$
You will get:
$2\int\frac{1}{\sqrt{1-u^2}}.du$
$=2sin^{-1}(u)+c$
$=2sin^{-1}(\sqrt{x})+c$

Logged

airline

Victorian
Trailblazer
Posts: 49
Respect: +1

Re: Anti-Diff Help

« Reply #2 on: May 08, 2009, 07:41:32 pm »

0

sorry...but I still don't get it..."du"??

Logged

TrueTears

TT
Honorary Moderator
Great Wonder of ATAR Notes
Posts: 16363
Respect: +667

Re: Anti-Diff Help

« Reply #3 on: May 09, 2009, 01:05:52 am »

0

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'

Logged

PhD @ MIT (Economics).

Interested in asset pricing, econometrics, and social choice theory.

Recent Posts

Re: Accelerated VCE reasoning by Aaron (VIC Year 9 Discussion): July 22, 2022, 06:38:54 pm
Accelerated VCE reasoning by leeknow2 (VIC Year 9 Discussion): July 22, 2022, 06:14:52 pm
Re: English Extension 1 Resources Thread by FloraD (HSC English Extension 1): July 22, 2022, 06:09:01 pm
Re: 35 study score after bombing 2 SACs? by james.358 (VCE Mathematical Methods CAS): July 22, 2022, 03:10:24 pm
35 study score after bombing 2 SACs? by Ickajock (VCE Mathematical Methods CAS): July 22, 2022, 02:04:47 pm
Re: SHS Exam 2023, What timing slot by HiKal (Selective Schools Admissions Tests): July 22, 2022, 10:41:33 am
Re: Exam is practically tomorrow lolll by HiKal (Selective Schools Admissions Tests): July 22, 2022, 10:40:47 am
Re: Photosynthesis by angelabean (VCE Biology): July 22, 2022, 10:12:54 am
Re: Exam is practically tomorrow lolll by AAAHHHpraying (Selective Schools Admissions Tests): July 22, 2022, 09:43:27 am
Re: VCE English Language Question Thread by schoolstudent115 (VCE English Language): July 22, 2022, 12:09:02 am

Print

Pages: [1] Go Up