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

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1. 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. 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. (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. Another approach can be to express as
5. (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. (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.
7. (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...
8. (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. ok I am still not getting the right answer for this, am I on the right lines?

10. (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. (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.
12. 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. (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. (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. ok, yes I have it!!! woohoo !!!!!!!!!!

Thank you both so much.

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