Another integration Q

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: Another integration Q (Read 587 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

sajib_mostofa

Victorian
Forum Leader
Posts: 829
Respect: +6

Another integration Q

« on: October 25, 2010, 08:14:48 pm »

0

These sort of Q's really annoy the hell outta me
Using the substituion $u=\sqrt{x}$ , Find $\int \frac{\sqrt{x}}{x+1} dx$

« Last Edit: October 25, 2010, 08:19:00 pm by sajib_mostofa »

Logged

brightsky

Victorian
ATAR Notes Legend
Posts: 3136
Respect: +200

Re: Another integration Q

« Reply #1 on: October 25, 2010, 08:20:31 pm »

0

Remember u^2 = x.

For full integration:

Sub $u = \sqrt{x}$ , $du = \frac{1}{2\sqrt{x}} dx$

Integrand becomes -

$2 \int \frac{u^2}{u^2 + 1} du$

$= 2 \int \left(1 - \frac{1}{u^2 + 1}\right) du$

$= 2u - 2 \int \frac{1}{u^2 + 1} du$

$= 2u - 2 \arctan(u) + C$

Sub everything back in:

$= 2\sqrt{x} - 2 \arctan(\sqrt{x}) + C$

« Last Edit: October 25, 2010, 08:25:58 pm by brightsky »

Logged

2020 - 2021: Master of Public Health, The University of Sydney
2017 - 2020: Doctor of Medicine, The University of Melbourne
2014 - 2016: Bachelor of Biomedicine, The University of Melbourne
2013 ATAR: 99.95

Currently selling copies of the VCE Chinese Exam Revision Book and UMEP Maths Exam Revision Book, and accepting students for Maths Methods and Specialist Maths Tutoring in 2020!

sajib_mostofa

Victorian
Forum Leader
Posts: 829
Respect: +6

Re: Another integration Q

« Reply #2 on: October 25, 2010, 08:25:13 pm »

0

Could you care to explain why there is a 2 outside the integral sign and the top part of the fraction is $u^2$ (in the first step)?

« Last Edit: October 25, 2010, 08:41:08 pm by sajib_mostofa »

Logged

m@tty

Victorian
ATAR Notes Legend
Posts: 4324
Respect: +33
School: Heatherton Christian College
School Grad Year: 2010

Re: Another integration Q

« Reply #3 on: October 25, 2010, 08:57:21 pm »

0

$I=\int\frac{\sqrt{x}}{x+1}dx$

Now you're making the substitution for u:

$I=2\int \frac{x}{x+1}\cdot \frac{1}{2\sqrt{x}}dx$

$x=u^2$ and $du=\frac{1}{2\sqrt{x}}dx$

$\implies I=2\int \frac{u^2}{u^2+1}du$

Logged

2009/2010: Mathematical Methods(non-CAS) ; Business Management | English ; Literature - Physics ; Chemistry - Specialist Mathematics ; MUEP Maths

96.85

2011-2015: Bachelor of Aerospace Engineering and Bachelor of Science, Monash University

2015-____: To infinity and beyond.

sajib_mostofa

Victorian
Forum Leader
Posts: 829
Respect: +6

Re: Another integration Q

« Reply #4 on: October 25, 2010, 08:58:57 pm »

0

Cheers for that M@tty

Logged

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