What is laplacetransform (t^2)/2 ?

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

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laplacetransform (t^2)/2

laplace transform

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

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

Solution steps

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

\int e^{- s t} (2 t + 1) d t

y = \frac{1}{x ^{2}}, y = x, y = \frac{1}{8} x

\frac{d}{d x} (50 e^{- 0.5 x} - (\frac{5}{x}))

\frac{\partial}{\partial x} (x + e^{4 y})

\int \frac{( 3 x + 4 )}{( x ^{2} + 4 ) ( 3 - x )} d x

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