What is laplacetransform 12t^3-t^2 ?

The answer to laplacetransform 12t^3-t^2 is (72)/(s^4)-2/(s^3)

Popular >

laplacetransform 12t^3-t^2

laplace transform

12 t^{3} - t^{2}

\frac{72}{s ^{4}} - \frac{2}{s ^{3}}

Solution steps

L {12 t^{3} - t^{2}}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 12 L {t^{3}} - L {t^{2}}

L {t^{3}} : \frac{6}{s ^{4}}

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

= 12 \cdot \frac{6}{s ^{4}} - \frac{2}{s ^{3}}

Refine

12 \frac{6}{s ^{4}} - \frac{2}{s ^{3}} : \frac{72}{s ^{4}} - \frac{2}{s ^{3}}

= \frac{72}{s ^{4}} - \frac{2}{s ^{3}}

\frac{d}{d x} (2 x - \frac{4}{x})

\int \frac{2 x ^{3} - 4 x ^{2} - 9 x - 1}{x ^{2} - 2 x - 5} d x

\int \frac{x ^{2}}{81 + x ^{2}} d x

\int_{0}^{1} sin (π \cdot x) d x

x \to 3 lim (\frac{x ^{2} - 2}{x - 3})

What is laplacetransform 12t^3-t^2 ?
The answer to laplacetransform 12t^3-t^2 is (72)/(s^4)-2/(s^3)