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    (Original post by Ano123)
    Any ideas?
    Coincidentally enough I was learning about reduction formulae when you posted this and I got:

    I_n=\displaystyle \int _0^{\frac{1}{2} \pi } \cos^{n} x \ dx = \frac{n-1}{n} \cdot I_{n-2}

    Which would mean that

    \displaystyle I_{100}=\frac{\prod_{i=1}^{100} (2i-1)}{2(50!)} \cdot \frac{\pi}{2}

    To be honest I have no idea if I am correct or how to get it in the wanted form, so good luck.
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    (Original post by RDKGames)
    Coincidentally enough I was learning about reduction formulae when you posted this and I got:

    I_n=\displaystyle \int _0^{\frac{1}{2} \pi } \cos^{n} x \ dx = \frac{n-1}{n} \cdot I_{n-2}

    Which would mean that

    \displaystyle I_{100}=\frac{\Pi_{i=1}^{100} (2i-1)}{2(50!)} \cdot \frac{\pi}{2}

    To be honest I have no idea if I am correct or how to get it in the wanted form, so good luck.
    Your answer is not quite right. The answer is  \displaystyle \frac{ \pi \Gamma (100)}{2^{100} ( 50\Gamma ^2(50))} if it gives you a clue haha.
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    (Original post by B_9710)
    Your answer is not quite right. The answer is  \displaystyle \frac{ \pi \Gamma (100)}{2^{100} ( 50\Gamma ^2(50))} if it gives you a clue haha.
    Well, that's neat. I never came across that gamma function and notation before and I've no clue how to work with it nor how to get to that form.
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    (Original post by RDKGames)
    That would be the limit, yes. I think it would make more sense to rewrite it as:

    \int^b_a x^{-2} dx=\frac{1}{a}, 0<a<b, b\rightarrow \infty

    but I'm not sure. Something about limits should be in there anyway.
    Should be \displaystyle \int_a^{\infty} x^{-2} \, \mathrm{d}x = \lim_{b \to \infty} \int_a^b x^{-2} \, \mathrm{d}x
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    (Original post by RDKGames)
    Well, that's neat. I never came across that gamma function and notation before and I've no clue how to work with it nor how to get to that form.
    Basically you have to know how to get  \displaystyle \prod _{n=0}^{N} (2n+1) and  \displaystyle \prod _{n=0}^{N} 2n in terms of  N! . And because  \Gamma (x) = (x-1)! I just used it for banter.
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    Hi, whats a good textbook for OCR A2 Maths? I've heard the CGP guides aren't very good.
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    Is it unheard of for the second part of a two-part STEP question to be easier than the first part? That's what's going on with me with the question I'm currently on (can do the second part with ease but can't do the first part).
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    (Original post by Palette)
    Is it unheard of for the second part of a two-part STEP question to be easier than the first part? That's what's going on with me with the question I'm currently on (can do the second part with ease but can't do the first part).
    No, it's quite common. Especially if the second part is just checking some cool special case or something, whilst the first part is more general.
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    (Original post by DarkEnergy)
    Hi, whats a good textbook for OCR A2 Maths? I've heard the CGP guides aren't very good.
    Not familiar with OCR but.. I'd have hoped that the textbook was enough with maths it's all about practice, a good textbook should offer this as well as the learning material.. all you need (I hope the OCR textbooks do this as well as Edexcel does). You can probably find extension material online.
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    (Original post by SeanFM)
    Not familiar with OCR but.. I'd have hoped that the textbook was enough with maths it's all about practice, a good textbook should offer this as well as the learning material.. all you need (I hope the OCR textbooks do this as well as Edexcel does). You can probably find extension material online.
    I don't know if I'm being stupid (probably am) but I don't know what textbook people keep referring to, we were never told about any textbook in class or anything, only the CGP revision guides. Thanks for the reply.
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    (Original post by DarkEnergy)
    I don't know if I'm being stupid (probably am) but I don't know what textbook people keep referring to, we were never told about any textbook in class or anything, only the CGP revision guides. Thanks for the reply.
    I've just googled and I'm just as confused there doesn't seem to be a set textbook or even individual ones.. I see a few versions of ones that combine C3 and C4... interesting. Probably can't go too far wrong with any of those.

    Is this with MEI or Non-MEI?
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    (Original post by SeanFM)
    Is this with MEI or Non-MEI?
    Non-MEI
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    Im doing some questions on algebra & functions (first few C3 topics) but i dont have any answers :3
    Is anyone willing to mark them for me? - let me know and ill send a PM with the questions and my answers.
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    (Original post by kiiten)
    Im doing some questions on algebra & functions (first few C3 topics) but i dont have any answers :3
    Is anyone willing to mark them for me? - let me know and ill send a PM with the questions and my answers.
    Sure.
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    (Original post by RDKGames)
    Sure.
    Sorry someone already sent me a PM :/. But thank you anyway

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    Why is the integral of x/x^2 +1 =1/2 ln|x^2 +1| not sure what c4 method to use to get and understand this results
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    (Original post by youreanutter)
    Why is the integral of x/x^2 +1 =1/2 ln|x^2 +1| not sure what c4 method to use to get and understand this results
    Notice how the numerator is similar to the derivative of the denominator, and go from there.
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    (Original post by youreanutter)
    Why is the integral of x/x^2 +1 =1/2 ln|x^2 +1| not sure what c4 method to use to get and understand this results
    int(x/x^2+1) = 1/2int(2x/x^2+1) inside the integral we now have derivative over function so the integral becomes ln of the denominator ln(x^2+1) and the result is (1/2)ln(x^2+1) + C
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    (Original post by DarkEnergy)
    Non-MEI
    :hmmmm: strange that there is no set textbook.. sorry.
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    (Original post by SeanFM)
    :hmmmm: strange that there is no set textbook.. sorry.
    No problem, cheers for looking anyways. Reckon this will be alright? link
 
 
 
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