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# FP2, Chapter 1, Exercise 1 Question 1. Oh God, watch

1. (Original post by Clarity Incognito)
haha, I actually deceived myself into thinking that that might actually be quicker but alas, it is not. That method is actually rather long.
Working out the expansion is rather long. De Moivre's Theorem speeds it up.
2. (Original post by maxfire)
But pikachu aint real neither.

We should prbably stop derailing this thread
No. You did not. You did not just say that

Yeah, perhaps, perhaps not.
3. I swear this is in C4
4. (Original post by stevencarrwork)
Working out the expansion is rather long. De Moivre's Theorem speeds it up.
I still don't get why you are applying de moivre's theorem to such a simple integral.
5. (Original post by Krinkles)
I swear this is in C4
My method is, I don't particularly understand why people are applying de moivre's theorem to it presently though. That is fp2
6. (Original post by stevencarrwork)
Working out the expansion is rather long. De Moivre's Theorem speeds it up.
De Moivre's is the long way round when it's an odd power tbh.

Split the even powers into (1-(cosx)^2), then you always have a f'(x)f(x)^n.

OP: Have you covered the work in core 4 on calculus using trig? That will explain it a lot better than your FP2 book, it assumes you've already done core 4. (Well, my MEI book does.)
7. In my opinion, the OP had made a perfectly good start to the question by himself - a substitution of u = cos x would have got him home.
8. (Original post by Scallym)
De Moivre's is the long way round when it's an odd power tbh.

Split the even powers into (1-(cosx)^2), then you always have a f'(x)f(x)^n.

OP: Have you covered the work in core 4 on calculus using trig? That will explain it a lot better than your FP2 book, it assumes you've already done core 4. (Well, my MEI book does.)
Ya ya but you use that when you have bigger powers surely. This particular one does not require it.
9. (Original post by Clarity Incognito)
Ya ya but you use that when you have bigger powers surely. This particularly one does not require it.
I'm not really sure what you mean.
I would (personally) only use De Moivre's if the power's higher than 5, I find the standard trig identities quicker for lower powers.
10. (Original post by Scallym)
I'm not really sure what you mean.
I would (personally) only use De Moivre's if the power's higher than 5, I find the standard trig identities quicker for lower powers.
That's precisely what I mean i.e. this question didn't need de Moivres, then again, I realised that as it is in the FP2 book, they wanted you to use de moivres
11. (Original post by Clarity Incognito)
That's precisely what I mean i.e. this question didn't need de Moivres, then again, I realised that as it is in the FP2 book, they wanted you to use de moivres
Ah, right.
It's the first question in the book, so i doubt de moivres has been covered yet.
12. (Original post by Scallym)
Ah, right.
It's the first question in the book, so i doubt de moivres has been covered yet.
I think that that was probably a slight exaggeration! don't ask

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