Integration by Substitution


    Rep:


    I got parts a & b but there's something I want to ask in general but using this as an example. In part c) I have to do dx/du but how do I know when to do that? I'm sure it hasn't come up in all the papers but I tripped up on the question because I got up to :

    4/2 (b:a)[x^3(lnu)du] but didn't get past this stage till I went through it with Exam Solutions, can anyone tell me when to look out for it please

    Rep:
    You have

     \displaystyle \int x^3 \ln (x^2+2) \ dx

    and you need to change this to an integral du using the substitution \displaystyle u=x^2+2

    The way to change dx to du is to find du/dx:

     \displaystyle \frac{du}{dx} = 2x \implies dx = \frac{du}{2x}

    Now substutute everything in, remembering that x^2=u-2.

    Post your working if you're still stuck. Or post the specific part that confuses you.

    Rep:
    You have to do dx/du (or similar) for every substitution. It is how you change the dx into a du.

    Rep:
    Thank you both, I got it now

    I was getting confused before because I thought it was an additional step. One question though - when you're finding the area/volume of a curve using Integration and I know when they are parametric, you add a little bit after the integral of y^2 as in it'll dx/dt*dt or something?

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?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  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 the button to the right to create your account

    Slide to join now Processing…

: June 19, 2012

Which unis are the poshest?

See what students perceive to be the classiest establishments in Britain

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