Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    7
    ReputationRep:
    I was trying to integrate (2-1/x)^2

    Why do you need to expand this before you integrate? When i first tried i got 1/3(2-1/x)^3*x^-2

    This normally works. Why is this case an exception?
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by stolenuniverse)
    I was trying to integrate (2-1/x)^2

    Why do you need to expand this before you integrate? When i first tried i got 1/3(2-1/x)^3*x^-2

    This normally works. Why is this case an exception?
    The derivative of 2-\frac{1}{x} is not a constant therefore the reverse chain rule does not work here - substitution is required instead, or expansion as you said.
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by stolenuniverse)
    I was trying to integrate (2-1/x)^2

    Why do you need to expand this before you integrate? When i first tried i got 1/3(2-1/x)^3*x^-2

    This normally works. Why is this case an exception?
    You can only use reverse chain rule when the stuff in the brackets is linear i.e. is of the form ax+b.

    \displaystyle 2-\frac{1}{x} is non-linear.

    This is one of the worst understood topics in A Level so you're not alone
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    You can only use reverse chain rule when the stuff in the brackets is linear i.e. is of the form ax+b.

    \displaystyle 2-\frac{1}{x} is non-linear.

    This is one of the worst understand topics in A Level so you're not alone
    Or to put it another way, it's just a straight out stupid thing to teach at A-level. TBH whenever a post contains the words "reverse chain rule" it feels it's almost the poster will be using it incorrectly.
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by DFranklin)
    Or to put it another way, it's just a straight out stupid thing to teach at A-level. TBH whenever a post contains the words "reverse chain rule" it feels it's almost the poster will be using it incorrectly.
    I think it's fine to show it after teaching substitution so students can see why reverse chain rule works (although the "topic" shouldn't even be given a name IMO). Integrals of the form \int f(ax+b) \ dx are very common in C4 exams so it's useful to be able to integrate them quickly without writing out a substitution.

    The big problem is that reverse chain rule is right at the start of the integration chapter of the most popular textbook so most teachers teach it first. This always leads to problems when students try to use "reverse chain rule" for any integral.
    Offline

    15
    ReputationRep:
    You could only use reverse chain rule if you were integrating something like  \frac{1}{x^2}(1-1/x)^2 .
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by B_9710)
    You could only use reverse chain rule if you were integrating something like  \frac{1}{x^2}(1-1/x)^2 .
    In the Edexcel textbook, this is known as "integrating using standard patterns"

    In the textbook "reverse chain rule" is only for integrating f(ax+b).

    I was never taught any of these names so it took a while for me to get used to them when I first started tutoring.
    Offline

    15
    ReputationRep:
    (Original post by notnek)
    In the Edexcel textbook, this is known as "integrating using standard patterns"

    Reverse chain rule is only for integrating f(ax+b) but this may differ depending on the textbook.

    I was never taught any of these names so it took a while for me to get used to them when I first started tutoring.
    Well yeah I say the 'reverse chain rule' just because it's familiar to the user, but I don't know what's actually 'standard' terminology.
    Offline

    14
    ReputationRep:
    (Original post by DFranklin)
    TBH whenever a post contains the words "reverse chain rule" it feels it's almost certain the poster will be using it incorrectly.
    My thoughts exactly. That's why I thought I'd read this thread.
    Offline

    17
    ReputationRep:
    (Original post by notnek)
    I think it's fine to show it after teaching substitution so students can see why reverse chain rule works (although the "topic" shouldn't even be given a name IMO).
    Sure. But as you say, do it after you've done substitution and don't give it a name.

    It's kind of funny how the people who can consistently use "the reverse chain rule" correctly never call it that, while nearly every time someone posts that "I used the reverse chain rule", the chances are they've done so incorrectly.

    Of course, I'm probably falling into an "correlation does not imply causation" error myself here, but I really wish they wouldn't teach that particular piece of terminology...
    Offline

    11
    ReputationRep:
    (Original post by notnek)
    In the Edexcel textbook, this is known as "integrating using standard patterns"

    In the textbook "reverse chain rule" is only for integrating f(ax+b).

    I was never taught any of these names so it took a while for me to get used to them when I first started tutoring.
    How is the "reverse chain rule" defined? It merely sounds like a fancy name for substitution.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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