Results are out! Find what you need...fast. Get quick advice or join the chat
x

Unlock these great extras with your FREE membership

  • One-on-one advice about results day and Clearing
  • Free access to our personal statement wizard
  • Customise TSR to suit how you want to use it

Basic standard integral

Announcements Posted on
Had your SQA results? Find your uni forum to get talking to other applicants, existing students and your future course-mates 04-08-2015
Competition: win a karting session for you and seven mates! 24-07-2015
  1. Offline

    ReputationRep:
    Basically we have been given a sheet with all the standard integrals we should know.

    I don't however understand this one:

    Integral f'(g(x))g'(x)dx = f(g(x)) + c

    Would someone using latex just give an example using a simple equation as then I should see it much clearer!

    Thanks
  2. Offline

    ReputationRep:
    (Original post by TimothyTankT)
    Basically we have been given a sheet with all the standard integrals we should know.

    I don't however understand this one:

    Integral f'(g(x))g'(x)dx = f(g(x)) + c

    Would someone using latex just give an example using a simple equation as then I should see it much clearer!

    Thanks
    Use a substitution of u=g(x) and it should drop out. That integrand is in the form of the derivative of a composite function.
  3. Offline

    ReputationRep:
    (Original post by TimothyTankT)
    Basically we have been given a sheet with all the standard integrals we should know.

    I don't however understand this one:

    Integral f'(g(x))g'(x)dx = f(g(x)) + c

    Would someone using latex just give an example using a simple equation as then I should see it much clearer!

    Thanks
    It is the rule for the integration of compodite functions and the base of this notation
    is the definition of undetermined integral namely
    \displaystyle\int f(x)\ dx=F(x)+c so that
    [F(x)+C]'=f(x)
    from this
    \displaystyle \int f'(x)\ dx=f(x)+c
    If function f in composite, for example f(g(x)), then from the chain rule
    [f(g(x))]'=f'(g(x)\cdot g'(x) where f' is derivative of outer function
    substituting g(x) in x multiplied by the derivative of inner function, g'(x).
    So integrating this
    \int f'(g(x)) \cdot g'(x)\ dx=f(g(x))+C
    Generally
    \displaystyle\int h[u(x)]\cdot u'(x)\ dx=H[u(x)]+C where H is the primitive function of h.
    For example:
    \displaystyle\int -tanx\ dx=\int (-sinx)\frac{1}{cosx}\ dx=ln|cosx|+C
    because the primitive function of 1/x is ln|x| and the derivative of cosx is -sinx.
    F.e 2.
    \displaystyle\int \frac{1}{xlnx}\ dx=\int \frac{1}{x}\cdot\frac{1}{lnx}\ dx=ln|lnx|+C
    \displaystyle\int \frac{x}{1+x^4}\ dx=\frac{1}{2}\int 2x\frac{1}{1+(x^2)^2}\dx=\frac{1  }{2}arctan(x^2)+C
  4. Offline

    ReputationRep:
    Try differentiating f(g(x)). Use a substitution u = g(x).

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: October 28, 2010
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
SQA students: did you get the results you wanted today?
Results and Clearing

SQA results chat

Come talk about your results here

new on tsr

Indian? Join the society here

Take part in the chat and make friends

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

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