q determine the laplace transform for each of the

Question

Q. Determine the Laplace transform for each of the following functions from the basic de?nition of Equation.

(a) f₁(t) = u(t)

(b) f₂(t) = e-at

(c) f₃(t) = df (t) dt, assuming f (t) is transformable.

(d) f₄(t) = t

(e) f₅(t) = sin ωt

(f) f₆(t) = cos(ωt + θ)

(g) f₇(t) = te-at

(h) f₈(t) = sinh t

(i) f₉(t) = cosh t

(j) f₁₀(t) = 5f(t) + 2 df (t)