The Laplace transform of a single saw tooth pulse as shown

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The Laplace transform of a single saw tooth pulse as shown in figure—

1. 1 – 1 + 1 e^{– s}
  s s s²
2. 1 – 1 + 1 e^s
  s² s s²
3. 1 – 1 + 1 e^{– s}
  s² s s²
4. 1 – 1 - 1 e^{– s}
  s² s s²

Correct Option: C

L{f(t)} = ^∞₀ f(t)e^{– st} dt

= ∫¹₀ t e^{– st} dt

=		t	e^{– st}	– 1	e^{– st}		¹
			– s		s²		₀

=

e^{– s}

–

e^{– s}

–

0 –

1

– s

s²

s²

=	1	– e^{– s}		1	+	1
	s²			s		s²