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Integration by parts homework help

  • Thread starter Dustinsfl
  • Start date
699
5
[tex]\int_0^{infinity} \ e^{-s*t}*t*cos(t) dt[/tex]

I tried integration by parts with u=t*cost and dv=e^(-s*t) but that didn't get anywhere.

I then tried: [tex]\L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt[/tex] but again nothing was working.

This is a Laplace Transformation where ft=t cos(t)
 

Answers and Replies

gabbagabbahey
Homework Helper
Gold Member
5,001
6
Re: Integral

I then tried: [tex]\L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt[/tex] but again nothing was working.
Do you mean that you tried applying the rule

[tex]\mathcal{L}\{t^n g(t)\}=(-1)^n\frac{d^n}{ds^n}\mathcal{L}\{g(t)\}[/tex]

If so, that should be fairly easy, provided that you know what the Laplace transform of [itex]\cos(t)[/itex] is.
 
699
5
Re: Integral

The problem was I get cos(t)/(s*e^(-st)) which is in determinant and using l'hopitals rule didn't help.

Also, the integral after separation by parts is now e time sin then you get an in determinant form with sin.
 
gabbagabbahey
Homework Helper
Gold Member
5,001
6
Re: Integral

The problem was I get cos(t)/(s*e^(-st)) which is in determinant and using l'hopitals rule didn't help.
How on Earth are you getting something that depends on [itex]t[/itex] after integrating over [itex]t[/itex]? :confused:

Show your work so I can see where you are going wrong.
 
699
5
Re: Integral

Work

Both methods attempted

Never mind the image won't load.
 

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