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

    0
    ReputationRep:
    (Original post by OneMorePanda)
    Good luck integrating e^{x^2}.
    Actually I would make my u= e^x^2

    And dv= 6x


    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    (Original post by justinawe)
    y = e^{x^2}

    \ln y = \ln e^{x^2}

    \ln y = x^2

    Differentiating both sides w.r.t x:

    \dfrac{1}{y} \times \dfrac{dy}{dx} = 2x

    \dfrac{dy}{dx} = 2xy = 2xe^{x^2}


    Does this help you figure out how to integrate that?
    Sorry, no...Still lost. Like a cow on Astroturf.
    Offline

    0
    ReputationRep:
    (Original post by nm786)
    no don't expand it.
    How come? Is that a general rule for differential equations?
    Offline

    1
    ReputationRep:
    (Original post by nm786)
    sin^2xcos^2x =( \frac{1}{2}sin2x )^2 now expand the brackets and integrate.
    Hmm interesting i would tackle this q in a different much longer method lol im skacking in my speed of recognizing identities:/
    Offline

    2
    ReputationRep:
    (Original post by nm786)
    sin^2xcos^2x =( \frac{1}{2}sin2x )^2 now expand the brackets and integrate.
    What if it was 1/sin^2(x)cos^2(x) ?


    Posted from TSR Mobile
    Offline

    2
    ReputationRep:
    (Original post by justinawe)
    y = e^{x^2}

    \ln y = \ln e^{x^2}

    \ln y = x^2

    Differentiating both sides w.r.t x:

    \dfrac{1}{y} \times \dfrac{dy}{dx} = 2x

    \dfrac{dy}{dx} = 2xy = 2xe^{x^2}


    Does this help you figure out how to integrate that?

    can you not use the integration by parts straight away?
    Offline

    2
    ReputationRep:
    Did anyone get to the point where there was not enough time to attempt every single question on every single edexcel paper from several years ago and every soloman paper, so decided to just do the hard questions instead?

    I.e. leave out implicit diff and binomial and partial fractions and anything else that looked doable enough
    Offline

    0
    ReputationRep:
    (Original post by SortYourLife)
    Isn't that just (1/2x) e^x^2 ? :s


    Posted from TSR Mobile
    No, you could differentiate that to see that it isn't.
    Offline

    1
    ReputationRep:
    (Original post by OneMorePanda)
    Good luck integrating e^{x^2}.
    Lol im so undercooked atm how do you integrate that :/
    Offline

    14
    ReputationRep:
    (Original post by OneMorePanda)
    No, you could differentiate that to see that it isn't.
    Oh yeah :') you'd just use substitution wouldn't you?


    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    \displaystyle \int \frac{x}{x-2} \ dx

    QQ how would you split the above into partial fractions?
    Offline

    0
    ReputationRep:
    (Original post by überambitious_ox)
    Did anyone get to the point where there was not enough time to attempt every single question on every single edexcel paper from several years ago and every soloman paper, so decided to just do the hard questions instead?

    I.e. leave out implicit diff and binomial and partial fractions and anything else that looked doable enough
    exactly what I'm doing lmao - although I'm mainly just focusing on the big integration questions :P
    Offline

    0
    ReputationRep:
    when u get to the point where u have (0.5sin(2x))^2 u just use the double angle formula of cosine and then u integrate
    Offline

    0
    ReputationRep:
    (Original post by Rayquaza)
    Book shows to integrate by substitution but I'm lost.
    What don't you understand du=2x dx





    Posted from TSR Mobile
    Offline

    0
    ReputationRep:
    If you times an integral (with limits) by -1 do you swap the limits?
    Offline

    0
    ReputationRep:
    (Original post by SortYourLife)
    Oh yeah :') you'd just use substitution wouldn't you?


    Posted from TSR Mobile
    Yeah.

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

    QQ how would you split the above into partial fractions?
    I'm not sure if it's called partial fractions, but you can write the x in the numerator as x - 2 + 2.

    (Original post by Tikara)
    If you times an integral (with limits) by -1 do you swap the limits?
    Yeah.
    Offline

    0
    ReputationRep:
    (Original post by Myocardium)
    \displaystyle \int \frac{x}{x-2} \ dx

    QQ how would you split the above into partial fractions?
    you just add and subtract two! so x+2-2/x-2
    and this gives you 1+(2/x-2)
    Offline

    2
    ReputationRep:
    (Original post by Tikara)
    exactly what I'm doing lmao - although I'm mainly just focusing on the big integration questions :P
    ahaaa so it's not just me
    Offline

    0
    ReputationRep:
    (Original post by Rayquaza)
    Sorry, no...Still lost. Like a cow on Astroturf.
    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.

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

    QQ how would you split the above into partial fractions?
    \dfrac{x}{x-2} = \dfrac{x-2+2}{x-2} = \dfrac{x-2}{x-2}+\dfrac{2}{x-2} = 1+\dfrac{2}{x-2}
    Offline

    0
    ReputationRep:
    (Original post by Myocardium)
    \displaystyle \int \frac{x}{x-2} \ dx

    QQ how would you split the above into partial fractions?
    long division, hope this helps,
    Attached Images
     
 
 
 
Poll
Which Fantasy Franchise is the best?

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.