[vedderfan94]

Help please

f)Integrate: 36cos^3(3x) dx

It says to use double angle and triple angle formulas. I tried replacing cos(3x) with 4cos^3(x) - 3cosx but then it just becomes a horrible mess of algebra when I expand

[TenOfThem]

You can integrate

So you need to get it into that format

[vedderfan94]

(Original post by TenOfThem)
You can integrate

So you need to get it into that format

I don't know which formula to use though as there are several different ones and I just end up getting nowhere with the algebra and trig

[m1a1tank]

(Original post by vedderfan94)
I don't know which formula to use though as there are several different ones and I just end up getting nowhere with the algebra and trig

once you've got it in that format of sin^2(x)cos(x) you don't need a formula. You could just do it by recognition.

[Ree69]

You said so yourself:

Thus ...

...

...

And so ...

It's not that messy. (certainly not out of your reach)

[Ree69]

(Original post by TenOfThem)
You can integrate

I think integrals of that form might only be covered in FP3...

[m1a1tank]

(Original post by Ree69)
I think integrals of that form might only be covered in FP3...

no its definately covered in C4, i don't do further maths, but i learn't this format in C4

[Einy]

Its a standard pattern - it will be in c4 whatever course you do. But your teacher may have skipped over it, because you can use integration b y substituion to solve them instead.

[TenOfThem]

(Original post by Ree69)
I think integrals of that form might only be covered in FP3...

LoL

That is a standard integral and can be done by inspection or substitution

[Ree69]

(Original post by TenOfThem)
LoL

That is a standard integral and can be done by inspection or substitution

Of course, chain rule! (Well when you put it like that...)

I thought you were talking about the ability to immediately recognise that in practice (which is basically the same thing, just harder to notice - at least I certainly think so!)

[f1mad]

cos(3x) = 4cos^3(x) - 3cosx

cos^3(x)= 1/4(cos(3x)+3cosx)

36cos^3(x) = 9(cos(3x)+ 3cosx)

[m1a1tank]

yea can we try not to give the thread starter the solutions. We just help them out first and point them in the right direction so that they can try to figure it out on their own. then if they still after loads of tips not get it, then we should give the solution. right?

[TenOfThem]

(Original post by m1a1tank)
yea can we try not to give the thread starter the solutions. We just help them out first and point them in the right direction so that they can try to figure it out on their own. then if they still after loads of tips not get it, then we should give the solution. right?

To whom have you aimed this comment?

I only ask as no one has given the full solution

[m1a1tank]

(Original post by TenOfThem)
To whom have you aimed this comment?

I only ask as no one has given the full solution

no, sorry, was just making sure that no one would

[TenOfThem]

(Original post by m1a1tank)
no, sorry, was just making sure that no one would

Ah, ok