Edexcel A2 C4 Mathematics June 2016 - Official Thread

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

A little rude but fine nevertheless

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.

Did I say it was easy?

I did say by parts, but fair play anyways.

You go integrate $\displaystyle \int e^x \cosh(x) \ \mathrm{d} x$ by parts.

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

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?

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.

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 $a \to 1$.

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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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.

Yep, that's the way to do it.

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.