Mastering Integration: Strategies for Solving Tricky Equations

[kring_c14]

integration--im lost

Homework Statement

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, I am hopelessly stuck

 

[kring_c14]

uhmmm hi! i don't really know what to do...and blood is dripping out of my nose! waaaah! *dramatic*

 

[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.

 

[VietDao29]

Homework Statement

how do you integrate this one

$$\int sint cosnt dt$$


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

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

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, I am hopelessly stuck

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

 

[kring_c14]

Homework Statement

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

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

 

[kring_c14]

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

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

 

[VietDao29]

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

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? :)

 

[kring_c14]

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