The Laplace transform of a function is the function L (s) of the variable s defined by the improper integral (if it converges): Laplace

The Laplace transform of a function ƒ is the function L ƒ(s) of the variable s defined by the improper integral (if it converges):

Laplace transforms are widely used in physics and engineering.

Show that if ƒ(x) = sin αx, then

Lf(s) = * f(x)e~** dx