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    practice, practice and practice. Ive not sat down and memorised any of the integrals but i can recall any one of them instantly in a question due to the amount of practice I've done.
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    (Original post by Philip-flop)
    OMG!! Why couldn't I see that?? Thank you so much!
    I think you may get stuck after doing that and cancelling.

    A better method is to split up the fraction at the beginning and you'll be left with two integrals that will be in the formula book.
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    (Original post by notnek)
    I think you may get stuck after doing that and cancelling.

    A better method is to split up the fraction at the beginning and you'll be left with two integrals that will be in the formula book.
    So I would do?...
     \int (\frac{1 - sin x}{cos^2 x})dx

     = \int (\frac{1}{cos^2 x} - \frac{sinx}{cos^2 x})dx

     = \int [(\frac{1}{cos x})^2 - \frac{sinx}{cos x} \frac{1}{cos x}] dx

     = \int (sec^2x - tanx secx) dx

     = tan x - sec x + c


    (^Yes that took me ages to type in latex notation haha)

    How do you know what kind of "route" to take when working out equations involving trig identities and derivatives etc? I honestly wouldn't have known how to do this without any help
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    (Original post by Philip-flop)
    So I would do?...
     \int (\frac{1 - sin x}{cos^2 x})dx

     = \int (\frac{1}{cos^2 x} - \frac{sinx}{cos^2 x})dx

     = \int [(\frac{1}{cos x})^2 - \frac{sinx}{cos x} \frac{1}{cos x}] dx

     = \int (sec^2x - tanx secx) dx

     = tan x - sec x + c


    (^Yes that took me ages to type in latex notation haha)

    How do you know what kind of "route" to take when working out equations involving trig identities and derivatives etc? I honestly wouldn't have known how to do this without any help
    This is a hard question and it really isn't obvious which route to take unless you have had a lot of practice.

    The method you used with the identity then difference of two squares was "nice" in a way and could have ended well, you were just a bit unlucky this time But if you reach a dead end in one of these questions, just start again with a different route.

    Trying to end up with standard integrals (like in this question) is an approach that you should have in your mind as a possibility for these questions.


    Taking your initial route by the way would have got you to this point:

    \displaystyle \int \frac{1}{1+\sin x} \ dx

    which is simpler than what you started with but can't be integrated. Interestingly, if you were given the integral above then the best method is to multiply top and bottom by 1-\sin x to end up with your integral.
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    (Original post by notnek)
    This is a hard question and it really isn't obvious which route to take unless you have had a lot of practice.
    I was afraid you were going to say that!!

    (Original post by notnek)

    \displaystyle \int \frac{1}{1+\sin x} \ dx

    Interestingly, if you were given the integral above then the best method is to multiply top and bottom by 1-\sin x to end up with your integral.
    Yeah I get you! Like if... \displaystyle \int \frac{1}{1+\sin x} \ dx was an actual question then I would have to multiply top and bottom by 1-\sin x which will then eventually lead on to giving...

     \int (\frac{1 - sin x}{cos^2 x})dx

    then integrate etc from there, which I worked out to be...
     = tan x - sec x + c
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    (Original post by Philip-flop)
    I was afraid you were going to say that!!



    Yeah I get you! Like if... \displaystyle \int \frac{1}{1+\sin x} \ dx was an actual question then I would have to multiply top and bottom by 1-\sin x which will then eventually lead on to giving...

     \int (\frac{1 - sin x}{cos^2 x})dx

    then followed on from there, which I worked out to be...
     = tan x - sec x + c
    That's correct. I doubt you would get a question as hard as that in the exam without some guidance in the question.
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    (Original post by notnek)
    That's correct. I doubt you would get a question as hard as that in the exam without some guidance in the question.
    I hope so!!

    Saying that, all these types of questions are difficult for me. You know how much I struggled with this kind of stuff during C3 Differentiation, but now it's integration
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    So I've come to the conclusion that I really suck when it comes to trigonometry identities etc.

    I'm can't even do part (a)!!
    I'm assuming it's to do with one of those addition formulae trig identities?

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    (Original post by Philip-flop)
    So I've come to the conclusion that I really suck when it comes to trigonometry identities etc.

    I'm can't even do part (a)!!
    I'm assuming it's to do with one of those addition formulae trig identities?

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    Experiment. If you stick at a problem long enough, your problem solving skills will increase substantially.
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    (Original post by Naruke)
    Experiment. If you stick at a problem long enough, your problem solving skills will increase substantially.
    I honestly don't even know where to start with part (a) though

    Could it have something to do with factor formulae?
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    (Original post by Philip-flop)
    I honestly don't even know where to start with part (a) though

    Could it have something to do with factor formulae?
    try using factor formulae it might work it might not
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    (Original post by Philip-flop)
    I honestly don't even know where to start with part (a) though

    Could it have something to do with factor formulae?
    Sounds like a good idea to try. Why don't you try it and see where it leads you.
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    (Original post by Philip-flop)
    I honestly don't even know where to start with part (a) though

    Could it have something to do with factor formulae?
    I'm sorry if I sound harsh, but choosing the right technique to tackle an integral is half the battle and that takes plenty of practice!
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    (Original post by Naruke)
    I'm sorry if I sound harsh, but choosing the right technique to tackle an integral is half the battle and that takes plenty of practice!
    No you're right, I think this is one of those things that I just have to keep practising until the penny drops. Just finding it so so so difficult
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    (Original post by Philip-flop)
    Just finding it so so so difficult
    The thing with integration is that to be able to do it well, you really need to be happy with nearly all the other concepts you've been covering C3/C4. You need to know all the trig identities, and not just in a "I can use the factor theorem if I'm told I need to use it", but in a "I can see that the factor thereon might help here". You need to be reasonably fluid with differentiation.

    The good news is that if you're able to do all the integration you get in C4, suddenly all the trig/differentiation work will seem much easier, because you've gained so much practice in it. Also be aware that everyone is in the same boat and unless they've been really keeping on top of the previous topics, they'll be having the same issues.
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    (Original post by DFranklin)
    The thing with integration is that to be able to do it well, you really need to be happy with nearly all the other concepts you've been covering C3/C4. You need to know all the trig identities, and not just in a "I can use the factor theorem if I'm told I need to use it", but in a "I can see that the factor thereon might help here". You need to be reasonably fluid with differentiation.

    The good news is that if you're able to do all the integration you get in C4, suddenly all the trig/differentiation work will seem much easier, because you've gained so much practice in it. Also be aware that everyone is in the same boat and unless they've been really keeping on top of the previous topics, they'll be having the same issues.
    Yes that's exactly it, I'm not very confident with all the topics from C3 and C4 (especially when it comes to trigonometry!) which is why I'm struggling atm as everything from the previous topics seems included in this last chapter like trigonometry and partial fractions etc.

    Thanks for the reassurance, it's nice to think that there are others out there who are struggling to recall everything from previous topics too! Just hope I can eventually make everything stick in my head!
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    (Original post by Philip-flop)
    Yes that's exactly it, I'm not very confident with all the topics from C3 and C4 (especially when it comes to trigonometry!) which is why I'm struggling atm as everything from the previous topics seems included in this last chapter like trigonometry and partial fractions etc.

    Thanks for the reassurance, it's nice to think that there are others out there who are struggling to recall everything from previous topics too! Just hope I can eventually make everything stick in my head!
    You can't make it stick in your head, this is not history, geography, sociology or any subject like that. You have to understand what's actually going on, which is something the Edexcel textbooks can't help you with. I recommend you use other resources if you'd like somewhat of a deeper understanding.
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    (Original post by Naruke)
    You can't make it stick in your head, this is not history, geography, sociology or any subject like that. You have to understand what's actually going on, which is something the Edexcel textbooks can't help you with. I recommend you use other resources if you'd like somewhat of a deeper understanding.
    Yeah true. What kind of resources do you use to gain a deeper understanding? I have no idea how some of you mathematicians learn about the subject inside out. You're right though, the edexcel textbook don't explain things in enough depth it merely only shows you how to do things
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    (Original post by Philip-flop)
    Yeah true. What kind of resources do you use to gain a deeper understanding? I have no idea how some of you mathematicians learn about the subject inside out.
    So, for complicated reasons, I took Maths A level twice, even though I got an A the first time (and this was before A* was a grade, so A was highest possible).

    When I did it the first time, my integration was so-so; I could usually do the questions, but not 100% of the time.

    The next year, I was preparing for Cambridge entrance, and one of the things I did was go through all (or nearly all) the integration exercises in Bostock and Chandler. I don't remember exactly how many there were, but we're definitely talking 100s. By the end of that, I could integrate pretty well, and I knew all the trig identities by heart too! The A-level questions were a breeze that year!

    But there's no getting round that it was a lot of work and took a lot of time.
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    (Original post by DFranklin)
    So, for complicated reasons, I took Maths A level twice, even though I got an A the first time (and this was before A* was a grade, so A was highest possible).

    When I did it the first time, my integration was so-so; I could usually do the questions, but not 100% of the time.

    The next year, I was preparing for Cambridge entrance, and one of the things I did was go through all (or nearly all) the integration exercises in Bostock and Chandler. I don't remember exactly how many there were, but we're definitely talking 100s. By the end of that, I could integrate pretty well, and I knew all the trig identities by heart too! The A-level questions were a breeze that year!

    But there's no getting round that it was a lot of work and took a lot of time.
    Damn, I feel sorry for those poor integrals...
 
 
 
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