Given that $$F\left( s \right)$$  is the one-side Laplace transform of $$f\left( t \right),$$  the Laplace transform of $$\int_0^t {f\left( \tau \right)d\tau } $$   is

Given that $$F\left( s \right)$$  is the one-side Laplace transform of $$f\left( t \right),$$  the Laplace transform of $$\int_0^t {f\left( \tau \right)d\tau } $$   is Correct Answer $$\frac{1}{s}F\left( s \right)$$

Related Questions

Laplace transform of the function f(t) is given by $${\text{F}}\left( {\text{s}} \right) = {\text{L}}\left\{ {{\text{f}}\left( {\text{t}} \right)} \right\} = \int_0^\infty {{\text{f}}\left( {\text{t}} \right){{\text{e}}^{ - {\text{st}}}}{\text{dt}}{\text{.}}} $$       Laplace transform of the function shown below is given by
Transform Theory mcq question image
Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$   is
If F(s) is the Laplace transform of function f(t), then Laplace transform of $$\int\limits_0^{\text{t}} {{\text{f}}\left( \tau \right){\text{d}}\tau } $$   is
The input x(t) and output y(t) of a system are related as $$y\left( t \right) = \int\limits_{ - \infty }^t {x\left( \tau \right)} \cos \left( {3\tau } \right)d\tau .$$     The system is
The Laplace transform of f(t) = sin πt is $$F\left( s \right) = \frac{\pi }{{{s^2}\left( {{s^2} + {\pi ^2}} \right)}},\,s > 0.$$     Therefore, the Laplace transform of t sin πt is