find the laplace transforms when f(t)=e^(6t) if 05 Can anyone help?

Question

find the laplace transforms when f(t)=e^(6t) if 0<t<5 and 1 if t>5   Can anyone help?

amistre64 · Answer

$$\large\left.L\{e^{6t}\}\right|_{0}^{5}+\left.L\{1\}\right|_{5}^{inf}$$

amistre64 · Answer

$$e^{6t}\to\ e^{(6-s)t} =\frac{e^{(6-s)5}}{6-s}-\frac{e^{(6-s)0}}{6-s}$$$$1\to\ e^{-st} =\frac{e^{-sinf}}{-s}-\frac{e^{-s5}}{-s}$$

anonymous · Answer

isnt e^-sinf be equal to zero then?

amistre64 · Answer

yes, unless theyve altered reality when i wasnt looking :)

anonymous · Answer

so the answer would be e^((6-s)5)/(6-s)-1/(6-s)+e^(-s5)/s would that be correct?

amistre64 · Answer

that last bit should be a -

and you might wana simplify for good measure; but yes

amistre64 · Answer

i see, you took the - from teh s .. ok

anonymous · Answer

well you are deviding by -s so itd be positive. Thanks for the help though! :) It is greatly appreciated :)

amistre64 · Answer

yw :)