What is laplacetransform 4t^2 ?

The answer to laplacetransform 4t^2 is 8/(s^3)

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laplacetransform 4t^2

laplace transform

4 t^{2}

\frac{8}{s ^{3}}

Solution steps

L {4 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)}

= 4 L {t^{2}}

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

= 4 \cdot \frac{2}{s ^{3}}

Refine

4 \frac{2}{s ^{3}} : \frac{8}{s ^{3}}

= \frac{8}{s ^{3}}

\int 8 x^{4} - 5 x^{3} + 5 x^{2} + C d x

\int \frac{3 x ^{2} + 11 v}{v ^{2} - v - 6}

\int (2 x^{2} + 3) e^{6 x} d x

\frac{d}{d x} (\frac{4 x ^{3} - 5}{x ^{2} - 3})

x \to 0 - lim (\frac{6}{x})