Join TSR now and get all your revision questions answeredSign up now
    Offline

    0
    ReputationRep:
    Goodnight people best of luck

    Please get some sleep too , you don't want to be a zombie in the exam making silly mistakes due to tiredness!


    Posted from TSR Mobile
    • Welcome Squad
    Offline

    14
    ReputationRep:
    One thing about volumes which is annoying me, are we meant to know the volumes of spheres & cones or not? Because some people are saying we have to & others are saying we don't. I personally don't think so, they'de give us the formula for the volume in the Q wouldn't they? Need to get this cleared!

    EDIT: Doesn't matter any more
    Offline

    14
    ReputationRep:
    (Original post by Myocardium)
    \displaystyle \int \frac{x}{x-2} \ dx

    QQ how would you split the above into partial fractions?
    You can't do it into partial fractions..... You could do it so you have

    Name:  ImageUploadedByStudent Room1371508445.039930.jpg
Views: 151
Size:  108.6 KB


    Otherwise idk :s


    Posted from TSR Mobile
    Offline

    2
    ReputationRep:
    (Original post by Kieran?)
    What if it was 1/sin^2(x)cos^2(x) ?


    Posted from TSR Mobile
    same method but you will be left to integrate 4cosec^22x as you got a 1 on the numerator.

    (Original post by orange94)
    Would you integrate that by reverse chain rule

    Posted from TSR Mobile

    (Original post by fahmad1)
    please can anybody solve that for me sinx^2cosx^2 ?? Integration?????
    sin^2xcos^2x =( \frac{1}{2}sin2x )^2 dx now expand the brackets and integrate.

    \displaystyle \int \frac {1}{4}sin^22x

    using the identity: \displaystyle \int sin^22x = \frac{-1}{2}cos4x + \frac{1}{2} the integral now becomes: \displaystyle \int \frac{-1}{8}cos4x + \frac{1}{8} dx = \frac{-1}{32}sin4x + \frac{x}{8} + C
    Offline

    0
    ReputationRep:
    (Original post by F1Addict)
    Suppose that e^{x^2} was a guess to the answer to the integral. To check if its right, you differentiate it to see if you get 6xe^{x^2}. You get 2xe^{x^2} instead. Its not exactly what you need, but its almost identical. How can you change the initial guess so when you do differentiate you get 6xe^{x^2}.

    Alternatively, a substitution of u=x^2. Its a longer way, but if you're more comfortable with it, then its the better way.
    I would do this, is it correct?
    Attached Images
     
    Offline

    0
    ReputationRep:
    (Original post by OneMorePanda)
    You've either written your variables incorrectly, or that's an almost nonsensical question.
    Unfortunately, this is not the case. My question correctly relies on you to do what i stated. To make it easier, dy/dx = e^-t dy/dt.

    Could you prove that before you find out the second derivative.
    Offline

    0
    ReputationRep:
    (Original post by nm786)
    no don't expand it.
    Is this a rule for differential equations, would you not get the same answer?
    Or is it just to make working simple?
    Offline

    0
    ReputationRep:
    (Original post by ITomI)
    I would do this, is it correct?
    Yep. :yy:

    (You did miss out the constant though, but I'm being picky. Don't forget this tomorrow though!. )
    Offline

    0
    ReputationRep:
    (Original post by OneMorePanda)
    Yeah.



    I'm not sure if it's called partial fractions, but you can write the x in the numerator as x - 2 + 2.



    Yeah.
    (Original post by F1Addict)
    Suppose that e^{x^2} was a guess to the answer to the integral. To check if its right, you differentiate it to see if you get 6xe^{x^2}. You get 2xe^{x^2} instead. Its not exactly what you need, but its almost identical. How can you change the initial guess so when you do differentiate you get 6xe^{x^2}.

    Alternatively, a substitution of u=x^2. Its a longer way, but if you're more comfortable with it, then its the better way.



    \dfrac{x}{x-2} = \dfrac{x-2+2}{x-2} = \dfrac{x-2}{x-2}+\dfrac{2}{x-2} = 1+\dfrac{2}{x-2}
    (Original post by SortYourLife)
    You can't do it into partial fractions..... You could do it so you have

    Name:  ImageUploadedByStudent Room1371508445.039930.jpg
Views: 151
Size:  108.6 KB


    Otherwise idk :s


    Posted from TSR Mobile
    Where is everyone getting the add 2 subtract 2 from?
    Offline

    0
    ReputationRep:
    (Original post by orange94)
    It's the same you get e^t when you differentiate


    Posted from TSR Mobile
    Nope.
    Offline

    0
    ReputationRep:
    (Original post by SortYourLife)
    You can't do it into partial fractions..... You could do it so you have

    Name:  ImageUploadedByStudent Room1371508445.039930.jpg
Views: 151
Size:  108.6 KB


    Otherwise idk :s


    Posted from TSR Mobile
    I'm sure you can do that by partial fractions!
    Offline

    0
    ReputationRep:
    (Original post by F1Addict)
    Yep. :yy:

    (You did miss out the constant though, but I'm being picky. Don't forget this tomorrow though!. )
    yeah haha my bad, just tired now, time to sleep I think thanks
    Offline

    0
    ReputationRep:
    (Original post by ITomI)
    long division, hope this helps,
    Yes it did thanks
    Offline

    0
    ReputationRep:
    (Original post by Chekz)
    Nope.



    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    (Original post by Myocardium)
    Where is everyone getting the add 2 subtract 2 from?
    Its just a trick. x+2-2 is still x, but writing it this way lets you easily split the fraction and simplify it into something you can integrate.

    I wrote more on this method here and here.
    Offline

    14
    ReputationRep:
    (Original post by Ohmydog)
    I'm sure you can do that by partial fractions!
    How though as you only have one thing on the bottom?


    I suppose you could make it so there's A/1 B/x-2 maybe....


    Posted from TSR Mobile
    Offline

    3
    ReputationRep:
    (Original post by otrivine)
    can you not use the integration by parts straight away?
    You'd need to know how to differentiate or integrate ex2 to do that anyway, so integrating by parts would be a waste of time.
    Offline

    14
    ReputationRep:
    (Original post by Myocardium)
    Where is everyone getting the add 2 subtract 2 from?
    To make it so part of it is the same as the bottom, so subtracting 2 from x (and making it 1)


    However you can't just change the expression so you have to add the 2 back on, so it's the same as the original expression.

    Then just split it up.


    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    (Original post by Ohmydog)
    I'm sure you can do that by partial fractions!
    Okay, I tried. You can't
    Did you see this sort of question come up in an exam paper? I've never done anything of the sort.
    Offline

    14
    ReputationRep:
    (Original post by Ohmydog)
    Okay, I tried. You can't
    Did you see this sort of question come up in an exam paper? I've never done anything of the sort.
    You can do it by long division so there is always ways round it, but changing the numerator to match the denominator then balancing out just makes it a little quicker.

    You never know you might have done a question like that but just not noticed you could do it that way and just did long division instead, sometimes it's clearer to see than others.

    Having said that I can't remember seeing a question like it in any paper I've done recently, I just remember being quickly shown how to do it in a lesson once aha


    Posted from TSR Mobile
 
 
 
Poll
Which web browser do you use?

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.