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1. Integrating
I know that:

∫(Sin2tCos t )

= Sin3t/3 (using the f'(x)f(x) method)

However if I rewrote the integral as:

∫((1-Cos2t)Cos t )
=∫(Cos t - Cos3t )

How would I integrate the Cos3t, is this possible using the methods in C1-C4?
2. Re: Integrating
(Original post by sabre2th1)
I know that:

∫(Sin2tCos t )

= Sin3t/3 (using the f'(x)f(x) method)

However if I rewrote the integral as:

∫((1-Cos2t)Cos t )
=∫(Cos t - Cos3t )

How would I integrate the Cos3t, is this possible using the methods in C1-C4?
split it up using double angel formula.
3. Re: Integrating
(Original post by Emissionspectra)
split it up using double angel formula.
How? I mean the double angle formulas deal with Cos2x
4. Re: Integrating
(Original post by sabre2th1)
I know that:

∫(Sin2tCos t )

= Sin3t/3 (using the f'(x)f(x) method)

However if I rewrote the integral as:

∫((1-Cos2t)Cos t )
=∫(Cos t - Cos3t )

How would I integrate the Cos3t, is this possible using the methods in C1-C4?
You need to write in terms of and

hint
Spoiler:
Show
cox(3t) = cos(2t+t)
Last edited by Fing4; 20-06-2012 at 14:04. Reason: Added t for x
5. Re: Integrating
(Original post by Fing4)
You need to write in terms of and

hint
Spoiler:
Show
cox(3t) = cos(2t+t)
Cos3x = Cos 3x ?

I didn't know that, could you show me how?

Thanks a lot
6. Re: Integrating
(Original post by sabre2th1)
Cos3x = Cos 3x ?

I didn't know that, could you show me how?

Thanks a lot
It doesn't. You need to write an expression for cos^3(x) in terms of cos(3x) and cosx. I'll help you start.

Cox(3x)=cos(2x+x)=cos2xcosx-sin2xsinx

Edit: Why the neg? I know this isn't the easiest way to integrate cos^3(x) but this is what the OP asked.
Last edited by Fing4; 07-07-2012 at 20:47.
7. Re: Integrating
(Original post by sabre2th1)
I know that:

∫(Sin2tCos t )

= Sin3t/3 (using the f'(x)f(x) method)

However if I rewrote the integral as:

∫((1-Cos2t)Cos t )
=∫(Cos t - Cos3t )

How would I integrate the Cos3t, is this possible using the methods in C1-C4?
If you're ever asked to integrate Cos3t you should just use the fact that Cos3t = Cos t(1-Sin2t)

So Cos3t = Cos t-(Cost)Sin2t which can easily be integrated.

As a general rule if you have sin or cos to the power of an even number use the double angle formula.

If they're to the power of an odd number use the method above i.e. take out a factor of sin or cos and then split the rest into Sin2t or Cos2t and use Sin2t = 1-Cos2t)and Cos2t = 1-Sin2t