Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    When using u substitution to evaluate an integral why is it possible to treat du/dx as a fraction and rearrange to replace dx?
    Offline

    2
    ReputationRep:
    you aren't treating it as a fraction any more than you do when you solve a differential equation, you are just changing the variable you are integrating with respect to. if you want a proper answer, you'll have to ask someone good i.e. nuodai
    • PS Helper
    Offline

    14
    PS Helper
    There are a few answers I can give to this question depending on the level you're working out. If you're doing A-level, the answer is "you just can". If you're doing anything higher, the answer really is that you can't except for notation's sake. So when we write u^2\, du = 2x\, dx we do so on the understanding that we're going to do something else with the equation, for example integrate both sides to give something like \displaystyle \int u^2\, du = \int 2x\, dx, or "divide through" by a differential to give something like u^2\dfrac{du}{dx} = 2x or u^2\dfrac{du}{dt} = 2x\dfrac{dx}{dt}. This is possible because rules like the chain rule make it possible.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by nuodai)
    There are a few answers I can give to this question depending on the level you're working out. If you're doing A-level, the answer is "you just can". If you're doing anything higher, the answer really is that you can't except for notation's sake. So when we write u^2\, du = 2x\, dx we do so on the understanding that we're going to do something else with the equation, for example integrate both sides to give something like \displaystyle \int u^2\, du = \int 2x\, dx, or "divide through" by a differential to give something like u^2\dfrac{du}{dx} = 2x or u^2\dfrac{du}{dt} = 2x\dfrac{dx}{dt}. This is possible because rules like the chain rule make it possible.
    thank you
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 27, 2010

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
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

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.