Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Sorry for yet another thread. I'm on a quest to do every integration question in my C4 text book... and I canne do this one:

    \int \frac{2}{\sqrt x (x - 4)} dx; u = \sqrt x

    This is what I've done:

    let u^2 = x (am I allowed to do this? b/c the question says u = \sqrt x)
    so 2u  du/dx = 1
    so 2u  du = dx

    u = \sqrt x=> x = u^2

    \int \frac{2}{u(u^2 - 4)} 2u  du

    = \int \frac{4u}{u^3 - 4u} du

    Then I got stuck. The answer is meant to be ln | \frac{\sqrt x - 2}{\sqrt x + 2} | + c

    Any ideas?
    Rep will be given
    Offline

    16
    ReputationRep:
    cancel u, split into partial fractions.

    and voila.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Prudence Slutsky)
    = \int \frac{4u}{u^3 - 4u} du
    Cancel a u on top and bottom, factorise the denominator and then use partial fractions.
    Offline

    0
    ReputationRep:
    This man speaks the truth.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by notnek)
    Cancel a u on top and bottom, factorise the denominator and then use partial fractions.
    So should I be getting \int \frac{4}{u^2 - 4}?
    Offline

    16
    ReputationRep:
    (Original post by Prudence Slutsky)
    So should I be getting \int \frac{4}{u^2 - 4}?
    yeah.

    this goes to \int \frac{4}{(u-2)(u+2)} whichn u can splitz into partial fractionz.

    since there are no u's A+B=0 so its pretty obvious what A and B are.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Totally Tom)
    yeah.

    this goes to \int \frac{4}{(u-2)(u+2)} whichn u can splitz into partial fractionz.

    since there are no u's A+B=0 so its pretty obvious what A and B are.
    Oooh, I know what to do now!


    Thanks everyone
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 14, 2008

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.