[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

[lukas1051]

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

[raheem94]

(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

[Lord of the Flies]

(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

It seems you have taken the complicated route.

Try considering by parts

EDIT: actually don't - to myself

[raheem94]

Another approach can be to express as

[notnek]

(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.

[notnek]

(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.

[Lord of the Flies]

(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...

[jackie11]

(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

[jackie11]

ok I am still not getting the right answer for this, am I on the right lines?

[Lord of the Flies]

(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

[notnek]

(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.

[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

[Lord of the Flies]

(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.

[notnek]

(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 .

[jackie11]

ok, yes I have it!!! woohoo !!!!!!!!!!

Thank you both so much.