Integration question

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: Integration question (Read 849 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

JackSonSmith

Victorian
Forum Obsessive
Posts: 288
"Failure is part of nature, success is man-made"
Respect: +4
School Grad Year: 2015

Integration question

« on: January 01, 2015, 09:16:53 pm »

0

Find an anti-derivative of 1 / (2x-1) ^3 with respect to x.

Answer is -1 / 4(2x-1) ^2 +c .

Could someone please show me how to solve? Thank-you.

Logged

2014: Psychology
2015: English | Methods | Chinese SL | Specialist | Physics

2016: Bachelor of Commerce - The University of Melbourne

Start where you are. Use what you have. Do what you can. – Arthur Ashe

keltingmeith

Honorary Moderator
Great Wonder of ATAR Notes
Posts: 5493
he/him - they is also fine
Respect: +1292

Re: Integration question

« Reply #1 on: January 01, 2015, 09:32:51 pm »

+3

$\frac{1}{(2x-1)^3}=(2x-1)^{-3}$

Now, for the anti-derivative, we add one to the power, divide by the new power, then divide by the chain:

$\int (2x-1)^{-3}\: dx=\frac{1}{-2}(2x-1)^{-2}\times \frac{1}{2}=\frac{-1}{4(2x-1)^2}$

More generally, the function $\frac{k}{(ax+b)^n}$ has anti-derivative $\frac{-k}{a(n-1)(ax+b)^{n-1}}$

Logged

Try out my study score calculator, request your subjects, and help give feedback if you've already completed VCE!

JackSonSmith

Victorian
Forum Obsessive
Posts: 288
"Failure is part of nature, success is man-made"
Respect: +4
School Grad Year: 2015

Re: Integration question

« Reply #2 on: January 02, 2015, 11:38:52 pm »

0

Thank-you. Is it x 1/2 or / 1/2 ?

Logged

2014: Psychology
2015: English | Methods | Chinese SL | Specialist | Physics

2016: Bachelor of Commerce - The University of Melbourne

Start where you are. Use what you have. Do what you can. – Arthur Ashe

keltingmeith

Honorary Moderator
Great Wonder of ATAR Notes
Posts: 5493
he/him - they is also fine
Respect: +1292

Re: Integration question

« Reply #3 on: January 03, 2015, 12:00:02 am »

0

Quote from: JackSonSmith on January 02, 2015, 11:38:52 pm

Thank-you. Is it x 1/2 or / 1/2 ?

It's /2, which is the same as *(1/2).

Logged

Try out my study score calculator, request your subjects, and help give feedback if you've already completed VCE!

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