- #1

Reshma

- 749

- 6

^{n}?

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]