# Laplace from first principles

## Homework Statement

Find, from first principles, the Laplace transform of f(t) = sin2(3t)

## Homework Equations

sin23t = 1/2(1-cost(6t))

L{SINat} = a/(s2 + a2)

## The Attempt at a Solution

s/2(s2 + 36)

What I want to ask is what does the first principles part mean? Is that asking me to integrate or look at the table of transforms? I don't quite understand what method I'm suppose to use for the transformation. Any light on this topic would be heavily appreciated.

Last edited:

HallsofIvy
$$L(f)(s)= \int_0^\infty e^{-sx}f(x)dx$$