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# Core Maths 4: Integration/Trig/double and triple angle formulae Tweet

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1. Core Maths 4: Integration/Trig/double and triple angle formulae
Hi there

Please could someone take a look at this and advise if I am on the right lines, and maybe give me a little nudge in the right direction to solve the question

Many thanks
Jackie
2. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
No you're going down the wrong route.

Express cos^3(x) as cos(x)cos^2(x) and go from there. If you're still stuck, I'll help you some more
3. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by jackie11)
Hi there

Please could someone take a look at this and advise if I am on the right lines, and maybe give me a little nudge in the right direction to solve the question

Many thanks
Jackie
You are correct till

Then how did you wrote,

What you have is

Hint for integrating
Spoiler:
Show

It is an integral of the form

So try differentiating
4. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
Another approach can be to express as
5. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by Lord of the Flies)
It seems you have taken the complicated route.

Try considering by parts
I think your route is also complicated.

The method that Lukas gave is the best way to tackle this question.
6. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by Lord of the Flies)
What method?

Also, I don't see how an integration by parts is more complicated than the stream of equations in the OP:

Without difficulty, by parts twice gives:

I don't mean the OP's method. I mean the method given by lukas1051:

Both of these integrals are easy. It is far quicker and "nicer" to do this rather than use integration by parts twice.
Last edited by notnek; 03-07-2012 at 10:09.
7. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by notnek)

It is far quicker and "nicer" to do this rather than use integration by parts.
Yes, just realised this...

Besides I made an idiotic mistake in my post so I'm going to leave now...
Last edited by Lord of the Flies; 03-07-2012 at 10:12.
8. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by raheem94)
You are correct till

Then how did you wrote,

What you have is

[/spoiler]
yes you are right, omg what a silly mistake to make haha
9. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
ok I am still not getting the right answer for this, am I on the right lines?

10. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by jackie11)
ok I am still not getting the right answer for this, am I on the right lines?
should remind you of something...

Hint:

Spoiler:
Show

11. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by jackie11)
ok I am still not getting the right answer for this, am I on the right lines?
You main mistake is in saying that

You can't split up a product in an integral like this. In general,

Instead, you need to integrate as one expression.

Try differentiating and see what you get. This should give you a big clue as to what the integral of is.
Last edited by notnek; 03-07-2012 at 14:43.
12. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
Using the chain rule, differentiating sin³ x gives me;

-3 sin² x cos x

So the integral of cos x sin² x is -1/3 sin³ x.

Am I on the right lines now? lol
13. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by jackie11)
Using the chain rule, differentiating sin³ x gives me;

-3 sin² x cos x

So the integral of cos x sin² x is -1/3 sin³ x.

Am I on the right lines now? lol
Almost - you made a sign mistake. The derivative of sin is cos, not -cos.
14. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
(Original post by jackie11)
Using the chain rule, differentiating sin³ x gives me;

-3 sin² x cos x

So the integral of cos x sin² x is -1/3 sin³ x.

Am I on the right lines now? lol
Almost, but the derivative of shouldn't have a negative sign since the derivative of is not .
15. Re: Core Maths 4: Integration/Trig/double and triple angle formulae
ok, yes I have it!!! woohoo !!!!!!!!!!

Thank you both so much.