Question

Is the laplace transform of a double integral is [F(s)]/[s^2]
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Answer 1

Answer on Question #48240, Engineering, Other

Question:

Is the laplace transform of a double integral is $[F(s)]/[s^2]$

Answer:

If $G(s) = \mathcal{L}\{g(t)\}$, then

$$\mathcal{L} \left\{ \int_{0}^{t} g(t) \, dt \right\} = \frac{G(s)}{s}$$

Now if we have $G'(s) = \mathcal{L}\{g'(t)\}$ and:

$$\mathcal{L} \left\{ \int_{0}^{t} g'(t) \, dt \right\} = \frac{G'(s)}{s}$$ $$g(t) = \int_{0}^{t} g'(t) \, dt \quad \text{and} \quad G(s) = \frac{G'(s)}{s}$$ $$\mathcal{L} \left\{ \int_{0}^{t} g(t) \, dt \right\} = \mathcal{L} \left\{ \int_{0}^{t} \int_{0}^{t} g'(t) \, dt \, dt \right\} = \frac{G(s)}{s} = \frac{G'(s)}{s^2}$$

Answer: yes, it is.

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