- #1
Reshma
- 749
- 6
Can someone help me out with the proof of the Laplace transform of the function tn?
I did have a go at this one.
[tex]L[t^n] = \int_0^{\infty} t^n e^{-st}dt[/tex]
[tex]= t^n\frac{-e^{-st}}{s}\vert_0^{\infty} + {1\over s}\int_0^{\infty} nt^{n-1}e^{-st}dt[/tex]
[tex]={n\over s}\int_0^{\infty} t^{n-1}e^{-st}dt[/tex]
[tex]={n\over s}L[t^{n-1}][/tex]
I am supposed to arrive at the result:
[tex]L[t^n] = \frac{(n+1)!}{s^{n+1}}[/tex]
I did have a go at this one.
[tex]L[t^n] = \int_0^{\infty} t^n e^{-st}dt[/tex]
[tex]= t^n\frac{-e^{-st}}{s}\vert_0^{\infty} + {1\over s}\int_0^{\infty} nt^{n-1}e^{-st}dt[/tex]
[tex]={n\over s}\int_0^{\infty} t^{n-1}e^{-st}dt[/tex]
[tex]={n\over s}L[t^{n-1}][/tex]
I am supposed to arrive at the result:
[tex]L[t^n] = \frac{(n+1)!}{s^{n+1}}[/tex]