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

1. Mkay,
I have to integrate sin^3(x)

Attached is my working thus far, any ideas?
Attached Images

2. lol! that made me laugh. i'm of no use but good luck! x
3. (Original post by tazzik)
Mkay,
I have to integrate sin^3(x)

Attached is my working thus far, any ideas?
You can split up sin^3x to sin^2x.sinx and further using an identity transform it into (1-cos^2x)sinx. Get where to go from there?
4. Have you covered De Moivres Theorem? That would make it hella simpler.

If not, inverse chain rule is a good method, if you take sin3x as (sinx)3.
5. (Original post by tazzik)
Mkay,
I have to integrate sin^3(x)

Attached is my working thus far, any ideas?
Haha, sorry, I didn't look at your attachment till after I posted.

Well, there's a general formula for when you integrate expressions like sinxcos^2x, it is the reverse of differentiation, can you see what might differentiate into sinxcos^2x?
6. (Original post by tazzik)
Mkay,
I have to integrate sin^3(x)

Attached is my working thus far, any ideas?
What is the expansion of sin(3x)?
7. (Original post by maxfire)
Have you covered De Moivres Theorem? That would make it hella simpler.

If not, inverse chain rule is a good method, if you take sin3x as (sinx)3.
Hey, I'm not sure if I'm missing something but how could you use de moivre's theorem for this?

Also, your sig has actually ruined a part of my soul, thanks!
8. (Original post by stevencarrwork)
What is the expansion of sin(3x)?
It's to the power of 3.
9. (Original post by Clarity Incognito)
It's to the power of 3.
Yes. I know.

What is the expansion of sin (3x), after which the question is a piece of cake.

The expansion of sin (3x) is 3 sin x - 4 (sin x)^3
10. (Original post by stevencarrwork)
Yes. I know.

What is the expansion of sin (3x), after which the question is a piece of cake.
Hold on a minute, how does that help?
11. (Original post by Clarity Incognito)
Hey, I'm not sure if I'm missing something but how could you use de moivre's theorem for this?

Also, your sig has actually ruined a part of my soul, thanks!
Ahh whoops I was thinking of something else
12. (Original post by Clarity Incognito)
can you see what might differentiate into sinxcos^2x?
Although I have now done this question through book reading and head bashing, worryingly, no, I cannot see what would differentiate to give that. It could be that I haven't done it yet, or more likely, I am having a mental block. What does differentiate to give that?
13. (Original post by Clarity Incognito)
Aha, well that's a little gem right there.
Glad to be of help. Once you have replaced sin^3 x in terms of sin x and sin 3x, it is really easy.
14. (Original post by tazzik)
Although I have now done this question through book reading and head bashing, worryingly, no, I cannot see what would differentiate to give that. It could be that I haven't done it yet, or more likely, I am having a mental block. What does differentiate to give that?
integrate it and see :>
15. (Original post by tazzik)
Although I have now done this question through book reading and head bashing, worryingly, no, I cannot see what would differentiate to give that. It could be that I haven't done it yet, or more likely, I am having a mental block. What does differentiate to give that?
Essentially there's a list of prescribed formulae for the trig functions which are found from finding patterns in what you get when you differentiate different things and then considering that integration is the opposite.

For this particular example, the harder part is obviously integrating -sinxcos^2x so we'll isolate it.

If you think about cos^3x. What's the differential of that? It's 3sinxcos^2x

but we want -sinxcos^2x. Now if you look at (-1/3)cos^3x, what do you get?

and from that we can draw the general formula (1/n+1)cos^n+1x as the integral of sinxcos^nx.
16. (Original post by maxfire)
Ahh whoops I was thinking of something else
Yeah, I think you were imagining things.

Pikachu should not be depicted in such a demeaning manner. I detest!
17. (Original post by stevencarrwork)
Glad to be of help. Once you have replaced sin^3 x in terms of sin x and sin 3x, it is really easy.
haha, I actually deceived myself into thinking that that might actually be quicker but alas, it is not. That method is actually rather long.
18. (Original post by Clarity Incognito)
Yeah, I think you were imagining things.

Pikachu should not be depicted in such a demeaning manner. I detest!
I get it.

Though really, it's like saying that santa shouldn't be depicted as a paedophile: he is, but we just have to shelter our kids from the truth. Well, I'm lashing out, here, with a controversial sig.
19. (Original post by maxfire)
I get it.

Though really, it's like saying that santa shouldn't be depicted as a paedophile: he is, but we just have to shelter our kids from the truth. Well, I'm lashing out, here, with a controversial sig.
Well, if we look past the fact that Santa's not real and that he wouldn't feasibly fit down a chimney, he would still have to be one helluva rich paedo. Wait, I don't think I have a point, alas, this is the poor state your sig has delivered unto me.
20. (Original post by Clarity Incognito)
Well, if we look past the fact that Santa's not real and that he wouldn't feasibly fit down a chimney, he would still have to be one helluva rich paedo. Wait, I don't think I have a point, alas, this is the poor state your sig has delivered unto me.
But pikachu aint real neither.

We should prbably stop derailing this thread

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