Compute the Laplace transtorm of f(x)050x8 Chapter 8 The Laplace Transform: Given a function f(x) we define its Laplace transform by: L[f(x)]=0exf(x)dx - L[1]=s1L[e21]=sa1L[cos(x)]=s2+2sL[f(x)]=sL[f(x)]f(0) - L[x]=s21L[sin(x)]=s2+2L[u(xc)]=semf(x)]=s2L[f(x)]sf(0)f(0) L[xf(x)]=dsdL[f(x)] P x[xn]=sn+1n!L[earf(x)]=F(sa)Leen1=(aa)21 - L[u(xc)f(x)]=ecf[(x+c)]c1[ecF(s)]=u(xc)f(xc)C[(xc)]=exc The Laplace trankform is linear: C[af+bg]=aC[f]+bL[g] - The inverse Laplace tranuform is linear: C1[aF(a)+bG(s)]=aC1[F(s)]+bC1[G(s)]