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Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of ∫₀^t f(τ)dτ is

1. sF(s) − f(0)
2. 1/s F(s)
3. ∫₀^t F(τ)dτ
4. 1/s [F(s) − f(0)]

Correct answer: 1/s F(s)

Solution

The Laplace transform of the integral of a function is given by the property that states the transform of the integral from 0 to t of f(τ) is equal to 1/s times the Laplace transform of f(t), which is represented as 1/s F(s). This reflects the relationship between integration in the time domain and multiplication by 1/s in the frequency domain.

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