Hey there! Sign in to join this conversationNew here? Join for free
    Offline

    5
    ReputationRep:
    (Original post by STATER)
    How do you integrate a product such as Sin2xSinx by parts? Apparently this can be done but I don't see how you can avoid an endless loop.
    Many thanks
    No need for integration by parts. Can manipulate to give:

    integral of: 2(sin^2 x)(cos x)

    The by inspection you can see this integral is 2/3sin^3 x
    Offline

    3
    (Original post by Gilo98)
    No need for integration by parts. Can manipulate to give:

    integral of: 2(sin^2 x)(cos x)

    The by inspection you can see this integral is 2/3sin^3 x
    I know that, but I am specifically interested in how to integrate it by parts.
    Offline

    5
    ReputationRep:
    (Original post by STATER)
    I know that, but I am specifically interested in how to integrate it by parts.
    Ah ok, jumped the gun a bit then. Was this an exam Q or just out of interest?
    Offline

    3
    (Original post by Gilo98)
    Ah ok, jumped the gun a bit then. Was this an exam Q or just out of interest?
    This was a june 2014 exam question (6iii). Since then, I've encountered a similar situation in third party practice paper where the solution was less obvious that in the 2014 Q, but integration by parts was an option. I'm just interested since a universal method is less of a headache and saves time.
    Offline

    5
    ReputationRep:
    (Original post by STATER)
    This was a june 2014 exam question (6iii). Since then, I've encountered a similar situation in third party practice paper where the solution was less obvious that in the 2014 Q, but integration by parts was an option. I'm just interested since a universal method is less of a headache and saves time.
    wonder how they marked those who went for above approach. I'd like to think if they pulled something like that in an edexcel paper they would at least point you in the direction of what to do.
    Offline

    3
    (Original post by Gilo98)
    wonder how they marked those who went for above approach. I'd like to think if they pulled something like that in an edexcel paper they would at least point you in the direction of what to do.
    I just don't know what I'm missing. Two questions where integration by parts seems impossible say " integration by parts twice" in the notes, and magically arrive at the solution.
    Offline

    5
    ReputationRep:
    (Original post by STATER)
    I just don't know what I'm missing. Two questions where integration by parts seems impossible say " integration by parts twice" in the notes, and magically arrive at the solution.
    Care to post a link? Seems silly to prevent someone from doing it in the simplest way
    Offline

    3
    (Original post by Gilo98)
    Care to post a link? Seems silly to prevent someone from doing it in the simplest way
    Take a look at Q3 part (b).
    http://madasmaths.com/archive/iygb_p...apers/c4_s.pdf

    solutions:


    http://madasmaths.com/archive/iygb_p..._solutions.pdf


    Also, here's the edexcel mark scheme for june 2014 (Q 6iii).

    https://a086a5a2f39bda93734c56a63fab...%20Edexcel.pdf

    Thanks
    Offline

    5
    ReputationRep:
    (Original post by STATER)
    Take a look at Q3 part (b).
    http://madasmaths.com/archive/iygb_p...apers/c4_s.pdf

    solutions:


    http://madasmaths.com/archive/iygb_p..._solutions.pdf


    Also, here's the edexcel mark scheme for june 2014 (Q 6iii).

    https://a086a5a2f39bda93734c56a63fab...%20Edexcel.pdf

    Thanks
    Tbf, looking at the edexcel mark scheme it seems they are not being picky as to what method you apply - 1 method mark for double angle formula and then 1 method mark for 'integrating to give asin^3 x. I can't seem to open the mark scheme for the other exam but looking at the question i cant find much which specifies a certain way in which to attack the integral. Would still like to see a worked example of integration by parts for it though, even if it is just out of interest :ahee:
    Offline

    14
    ReputationRep:
    (Original post by STATER)
    How do you integrate a product such as Sin2xSinx by parts? Apparently this can be done but I don't see how you can avoid an endless loop.
    Many thanks
    Name:  1432734000362.jpg
Views: 212
Size:  60.8 KB

    I left out all the "dx" to save space but I hope it's clear - after doing by parts twice you get the same integral as you started with as part of your integration and you make that the subject of the formula.

    Posted from TSR Mobile
    Offline

    3
    (Original post by aersh8)
    Name:  1432734000362.jpg
Views: 212
Size:  60.8 KB

    I left out all the "dx" to save space but I hope it's clear - after doing by parts twice you get the same integral as you started with as part of your integration and you make that the subject of the formula.

    Posted from TSR Mobile
    Nice one thanks. Disastrous failure on my part not to spot that.
    Offline

    14
    ReputationRep:
    (Original post by STATER)
    Nice one thanks. Disastrous failure on my part not to spot that.
    No worries it would be faster to just use angle addition formulae though
    Offline

    3
    (Original post by aersh8)
    No worries it would be faster to just use angle addition formulae though
    Yeah, it was just out of interest.
    Offline

    18
    ReputationRep:
    (Original post by STATER)
    Nice one thanks. Disastrous failure on my part not to spot that.
    Try e^x cosx
    Similar approach and it could be asked in an exam


    Posted from TSR Mobile
    Offline

    2
    ReputationRep:
    (Original post by physicsmaths)
    Try e^x cosx
    Similar approach and it could be asked in an exam


    Posted from TSR Mobile
    Hmm didn't know they expected you to know the integration by parts twice method and using the loop to substitute the original back in.

    I knew how to do that but my teacher said they wouldn't specifically require you to do that - so you could do questions like that but they would only ask a question that could be done without that method also.
    Offline

    18
    ReputationRep:
    (Original post by Tow)
    Hmm didn't know they expected you to know the integration by parts twice method and using the loop to substitute the original back in.

    I knew how to do that but my teacher said they wouldn't specifically require you to do that - so you could do questions like that but they would only ask a question that could be done without that method also.
    Well I know that integration by parts twice could come up definitely as I have seen it on a paper.It's good to know.


    Posted from TSR Mobile
    Offline

    2
    ReputationRep:
    (Original post by physicsmaths)
    Well I know that integration by parts twice could come up definitely as I have seen it on a paper.It's good to know.


    Posted from TSR Mobile
    Yeah definitely.

    But no question should require you to use the 'Loop' method.

    Integration by parts like this is fine:
    x^2sin(x)

    But integration by parts of this shouldn't come up:
    Sin(3x)cos(x)

    Unless you can rearrange to make it so that you can integrate it with using the loop method.
    Offline

    19
    ReputationRep:
    More C3/C4 Resources at
    http://www.thestudentroom.co.uk/show....php?t=3353445
    Offline

    13
    ReputationRep:
    Theres too much resources for maths, Im sturggling to do the exercises and edexcel papers alone lol
    Offline

    0
    ReputationRep:
    Hey I'm actually OCR but I couldn't find an OCR C4 2015 thread but I'm guessing you guys do vectors??
    Could someone help me with this question:

    Find a unit vector that is perpendicular to both 4i + 10j - 3k and 5i - 9j + 7k

    All I have so far is:
    4a + 10b - 3c = 0
    and
    5a - 9b + 7c = 0

    (ai + bj + ck being my unknown unit vector)

    Thanks
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?

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