# Integration-im lost

1. Sep 13, 2007

### kring_c14

integration--im lost

1. The problem statement, all variables and given/known data
how do you integrate this one

$$\int sint cosnt dt$$

i tried using this identity 1/2 [sin(t-nt) + sin (t-nt)]

then i got stuck so i used another identity again
sin (t$$^{+}_{-}nt$$)= sintcosnt$$^{+}_{-}$$costsinnt

the result is the original equation..

to sum it all, im hopelessly stuck

2. Sep 13, 2007

### kring_c14

uhmmm hi!!! i dont really know what to do...and blood is dripping out of my nose!! waaaah!! *dramatic*

3. Sep 13, 2007

### Dick

A sure fire way that doesn't take a lot of brains is to use identities like cos(x)=(exp(ix)-exp(-ix))/2 (deMoivre). You can convert the whole thing to exponentials and they are easy.

4. Sep 13, 2007

### VietDao29

Well, this identity doesn't look right to me.

Nope, you don't need to expand it. It'll give you the original expression. Hint: Can you simplify: t - nt, and t + nt?

5. Sep 13, 2007

### kring_c14

1/2 [sin(t+nt) + sin (t-nt)]--->sorry, got it wrong..this ones correct

6. Sep 13, 2007

### kring_c14

that gives me t$$^{2}$$-n$$^{2}$$t$$^{2}$$

but where would i plug this equation

im really not that good at manipulating equation..havent learned trigonometry at heart

7. Sep 13, 2007

### VietDao29

Ack. >"< No, that's not correct at all.

Well, it's not that hard. We have:

sin(t + nt) = sin[(n + 1)t]. Which can be easily integrated. Simple, eh? :)

You can do the same to the other one. Can you go from here? :)

8. Sep 13, 2007

### kring_c14

aw sorrryyy, lol...just being my dumb self again..shame on me.. lol
thank you very much!