The Laplace transform of a given wave

For the given waveform,

L{f(t)} = ∫^∞₀ f(t)e^{– st} dt
= ∫^T₀ 1·e– st dt + ∫ 2T T (– 1) e– stdt

=		e^{– st}			–		e^{– s}t		^2T
		– s					– s		_T

=	1	[e^{– st} – 1 – e^{– 2st} + e^{– st}]
	s

=	1	[1 – 2e^st + e^2st]
	s

=	1	(1 – e^{– sT})²
	s

	1	(1 – e^sT)²
	s