What is laplacetransform 1/2 t^2 ?

The answer to laplacetransform 1/2 t^2 is 1/(s^3)

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laplacetransform 1/2 t^2

laplace transform

\frac{1}{2} t^{2}

\frac{1}{s ^{3}}

Solution steps

L {\frac{1}{2} t^{2}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {t^{2}}

L {t^{2}} : \frac{2}{s ^{3}}

= \frac{1}{2} \cdot \frac{2}{s ^{3}}

Refine

\frac{1}{2} \frac{2}{s ^{3}} : \frac{1}{s ^{3}}

= \frac{1}{s ^{3}}

What is laplacetransform 1/2 t^2 ?
The answer to laplacetransform 1/2 t^2 is 1/(s^3)