Turn on thread page Beta
    • Thread Starter

    This is from the Heinneman textbook. If I'm lucky, maybe it'll be another misprint:

    "Use the substitution x=1/u to find the value of ∫(ln x*[1+x²]-1)dx between 2 and 1/2"

    Now, when you use the substitution, you end up with -∫(ln u*[1+u²]-1)dx between 1/2 and 2. This is exactly the same as the first integral, except with a minus sign in front of it and the limits swapped round, so the subsitution seems pretty pointless.

    The correct answer is 0. Can somebody explain how to get to it? Thanks.

    sorry, i tried it, but i'm not clever enough.

    Use the fact that:
    ab f(x) dx = - ba f(x) dx

    Your substitution showed that:
    I = -I

    So I must be zero.
    • Thread Starter

    (Original post by dvs)
    Use the fact that:
    ab f(x) dx = - ba f(x) dx

    Your substitution showed that:
    I = -I

    So I must be zero.
    Great - thanks, I thought it was something like that, but I couldn't work out how to show it in a decent way.
The home of Results and Clearing


people online now


students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
A-level students - how do you feel about your results?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


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