x Turn on thread page Beta
 You are Here: Home >< Maths

# integrate sin^3(x) watch

1. errr, no idea!
2. .
3. (Original post by Glutamic Acid)
.
can u carry on please...it's just a\bout confidence...i'd appreciate it.
4. (Original post by FoOtYdUdE)
can u carry on please...it's just a\bout confidence...i'd appreciate it.
Expand it out, we have

.

You can integrate the first term without difficulty, as for the second: what is the derivative of cos x? Can you see how this will help you integrate it?
5. Hokey-koke.

If you re-write it as:

Then you can use the identity:

So now you're trying to find:

Let us know how you get on with this.
If you want a hint about how to do that second term, just ask!
6. (Original post by Glutamic Acid)
Expand it out, we have

.

You can integrate the first term without difficulty, as for the second: what is the derivative of cos x? Can you see how this will help you integrate it?
-sinx? err and no
7. (Original post by FoOtYdUdE)
-sinx? err and no
Have you looked at integration by substitution?

Spoiler:
Show
If so, then is your substitution.

So

Can be written as

Also:

So

Or does the following look familiar:
8. (Original post by placenta medicae talpae)
Have you looked at integration by substitution?

Or does the following look familiar:
int by substn. yeah dun that.
9. oh im so silly..we can use parts for this quest.
10. (Original post by FoOtYdUdE)
oh im so silly..we can use parts for this quest.
Can do, yep

If you'd like to do it by substitution (which is probably easier!), you could take a peek at the spoiler in my last post?
11. (Original post by FoOtYdUdE)
oh im so silly..we can use parts for this quest.
You'll be forever using parts. Just use the chain rule. The derivative of cos^3(x) is -3sin(x)cos^2(x) so the integral of sinxcos^2(x) is -1/3cos^3(x).
12. A nice solution would be to use reduction formula....I can't remember it for (sinx)^n it's something like

For this substitute in n=3
13. (Original post by JamesyB)
A nice solution would be to use reduction formula....I can't remember it for (sinx)^n it's something like

For this substitute in n=3
What is ?
14. (sin^3X)/(3cos^2x)
this is the way I would do it, dunno if it's correct
15. (Original post by FoOtYdUdE)
oh im so silly..we can use parts for this quest.
The trick here is to spot derivatives. Try differentiating cos^3(x), what do you get? How does this relate to sin(x)cos^2(x)? How can you use your identities to manipulate this fact and use it?
16. (Original post by placenta medicae talpae)
What is ?
is used to mean Integral i.e.

is the integral you're working out where part of it is replaced by an n. In this case the squared part of the integral is changed to an n.

You can then work out a general form for integrating complicated functions (usually where integration by parts would be used multiple times) in terms of .

Sorry it's not very clear, only just learnt it at school so .... If anyone can explain it better then feel free
17. (Original post by JamesyB)
is used to mean Integral i.e.

is the integral you're working out where part of it is replaced by an n. In this case the squared part of the integral is changed to an n.

You can then work out a general form for integrating complicated functions (usually where integration by parts would be used multiple times) in terms of .

Sorry it's not very clear, only just learnt it at school so .... If anyone can explain it better then feel free
Oh right yeah, I get you.
This kind of thing is useful when trying to find things like:
isn't it.
18. (Original post by placenta medicae talpae)
Oh right yeah, I get you.
This kind of thing is useful when trying to find things like:
isn't it.
It is indeed
19. (Original post by JamesyB)
It is indeed
Cheers for that then; I had never come across that notation before!
I'll be using that in future, will I
20. If you're not confident with integrating by recognition, then after the initial sin^3 x = (1 - cos^2 x)sin x, just substitute u = cos x.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 16, 2010
Today on TSR

### Complete university guide 2019 rankings

Find out the top ten here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams