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Edexcel A2 C4 Mathematics June 2016 - Official Thread Watch

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    (Original post by EricPiphany)
    Did you try it though? It shouldn't really be on the C4 thread but whatever.
    I do Further Maths too so I knew how to do it

    \cosh(x) = \dfrac{e^{x}+e^{-x}}{2}

    After that it goes from an FP3 integral to a C4 integral
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    (Original post by edothero)
    I do Further Maths too so I knew how to do it

    \cosh(x) = \dfrac{e^{x}+e^{-x}}{2}

    After that it goes from an FP3 integral to a C4 integral
    I did say by parts, but fair play anyways.
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    (Original post by edothero)
    A little rude but fine nevertheless
    (Original post by EricPiphany)
    Did you try it though? It shouldn't really be on the C4 thread but whatever.
    It isn't as easy as either of you think, if I'm right.
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    (Original post by Zacken)
    It isn't as easy as either of you think, if I'm right.
    Did I say it was easy?
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    (Original post by EricPiphany)
    Did I say it was easy?
    Well, no - but I don't think parametrisation and taking limits is suitable for this thread.
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    (Original post by EricPiphany)
    I did say by parts, but fair play anyways.
    u = coshx
    dv/dx = e^x

    eventually youll end up with e^xcoshx again, which is the same as the original integral, so divide by 2

    .. I think
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    l give up.
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    (Original post by EricPiphany)
    You go integrate \displaystyle \int e^x \cosh(x) \ \mathrm{d} x by parts.
    Shouldn't really be on the C4 thread - so I'll knock this out:

    \displaystyle I_a = \int e^x \cosh ax \, \mathrm{d}x = e^x \cosh ax - a \int e^x \sinh ax \, \mathrm{d}x

    Hence: \displaystyle I = e^x \cosh ax - ae^x\sinh ax + a^2 I

    Then:

    \displaystyle I_1 = \lim_{a \to 1} \frac{e^x \cosh ax - ae^x \sinh ax}{(1-a)(1+a)} = \frac{1}{2}e^x\sinh x + \frac{x}{2} + \mathcal{C}
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    (Original post by edothero)
    u = coshx
    dv/dx = e^x

    eventually youll end up with e^xcoshx again, which is the same as the original integral, so divide by 2

    .. I think
    Nah (\cosh x)'' = \cosh x \neq -\cosh x so you're fukt.
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    (Original post by pecora)
    Perfect timing for the thread. Is there any point to resit an AS module if I got over 80% overall?
    In order to get the A*, do you absolutely need to get the 90% average in C3 and C4? Or could it also be a 90% average of the whole A-level?
    To get an A*, you need to get 90% AVERAGE in C3 and C4! )))
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    (Original post by Zacken)
    Shouldn't really be on the C4 thread - so I'll knock this out:

    \displaystyle I_a = \int e^x \cosh ax \, \mathrm{d}x = e^x \cosh ax - a \int e^x \sinh ax \, \mathrm{d}x

    Hence: \displaystyle I = e^x \cosh ax - ae^x\sinh ax + a^2 I

    Then:

    \displaystyle I_1 = \lim_{a \to 1} \frac{e^x \cosh ax - ae^x \sinh ax}{(1-a)(1+a)} = \frac{1}{2}e^x\sinh x + \frac{x}{2} + \mathcal{C}
    How do you take the limit? It doesn't look like it converges.
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    (Original post by EricPiphany)
    How do you take the limit? It doesn't look like it converges.
    \displaystyle

\begin{eqnarray*}\int e^x \cosh(x) dx &=& \lim_{a \rightarrow 1} \frac{ e^x \cosh(ax) - a e^x \sinh(ax)}{ (1 - a) (1 + a) }\\&=& \lim_{a \rightarrow 1} \frac{x e^x [ \sinh(ax) - a \cosh(ax)] - e^x \sinh(ax)}{-2}\\&=& \frac{1}{2} e^x\sinh(x) + \frac{1}{2} x\end{eqnarray*}

    Think about what \sinh x - \cosh x is in terms of exponentials and what tha means \frac{xe^x(\sinh x - a\cosh ax}{-2} is as a \to 1.
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    (Original post by Zacken)
    \displaystyle

\begin{eqnarray*}\int e^x \cosh(x) dx &=& \lim_{a \rightarrow 1} \frac{ e^x \cosh(ax) - a e^x \sinh(ax)}{ (1 - a) (1 + a) }\\&=& \lim_{a \rightarrow 1} \frac{x e^x [ \sinh(ax) - a \cosh(ax)] - e^x \sinh(ax)}{-2}\\&=& \frac{1}{2} e^x\sinh(x) + \frac{1}{2} x\end{eqnarray*}

    Think about what \sinh x - \cosh x is in terms of exponentials and what tha means \frac{xe^x(\sinh x - a\cosh ax}{-2} is as a \to 1.
    I'm just struggling with the assumption that the limit of the numerator is zero.
    I suppose we can make it so with an arbitrary constant.
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    Any ideas on what integrals could come up on the C4 paper this year ? I know there are loads but I haven't seen a question like 2sin3xcos2x in any of the UK C4 papers. Also, do you think that we will get a standard vector question or a vector question involving shapes such as circles or parallelograms ?
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    (Original post by Danllo)
    Any ideas on what integrals could come up on the C4 paper this year ? I know there are loads but I haven't seen a question like 2sin3xcos2x in any of the UK C4 papers. Also, do you think that we will get a standard vector question or a vector question involving shapes such as circles or parallelograms ?
    Integrals of a^x or stuff like
    Cos^3(x)sin(x).


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    (Original post by physicsmaths)
    Integrals of a^x or stuff like
    Cos^3(x)sin(x).


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    Can't you do that by recognition or something ...

    Like cos^3(x)sin(x) = -1/4cos^4(x)+c since you notice the derivative is next to it.

    Spoiler:
    Show
    I'm still a pleb at maths compared to you sensei!
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    (Original post by XxKingSniprxX)
    Can't you do that by recognition or something ...

    Like cos^3(x)sin(x) = -1/4cos^4(x)+c since you notice the derivative is next to it.
    Spoiler:
    Show
    I'm still a pleb at maths compared to you sensei!
    Yep, that's the way to do it.
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    (Original post by Zacken)
    Yep, that's the way to do it.
    :yeah: I'm finally getting somewhere in Maths :woohoo:

    I knew madasmaths would save me, speaking of which I scored my 1st A* in timed conditions = 96% -> 73/75 on C4 in 1 hour 18 mins with 12 mins to check over my work. I'm hoping to get it down to 1h 10 mins with 20 mins to check over my work.

    So far my averages have been: 86% (A), 87% (A), 96% (A*) + (x7 more Edexcel C4 papers + 11 Edexcel IAL + as many Madasmaths papers until real exam that I can fit)

    We're all gonna make it! :yep:
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    (Original post by XxKingSniprxX)
    Can't you do that by recognition or something ...

    Like cos^3(x)sin(x) = -1/4cos^4(x)+c since you notice the derivative is next to it.
    Spoiler:
    Show
    I'm still a pleb at maths compared to you sensei!
    Yeh bro like that
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    What about vector questions guys ? Do you think we will get a standard question or a question involving a shape like a octogenarian or some weird shape ?
    Do we need to know Newtons' law of cooling for differential equations?
 
 
 
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