laplacetransform 0.0796-0.066*x^{1/2}

Lösung

laplace transformation

0.0796 - 0.066 \cdot x^{\frac{1}{2}}

\frac{0.0796}{s} - \frac{0.066 π}{2 s ^{\frac{3}{2}}}

Schritte zur Lösung

L {0.0796 - 0.066 x^{\frac{1}{2}}}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

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

= L {0.0796} - 0.066 L {x^{\frac{1}{2}}}

L {0.0796} : \frac{0.0796}{s}

L {x^{\frac{1}{2}}} : \frac{π}{2 s ^{\frac{3}{2}}}

= \frac{0.0796}{s} - 0.066 \cdot \frac{π}{2 s ^{\frac{3}{2}}}

Fasse

\frac{0.0796}{s} - 0.066 \frac{π}{2 s ^{\frac{3}{2}}}

zusammen:

\frac{0.0796}{s} - \frac{0.066 π}{2 s ^{\frac{3}{2}}}

= \frac{0.0796}{s} - \frac{0.066 π}{2 s ^{\frac{3}{2}}}

\int_{0}^{1} 3 (1 + x)^{5} d x

\int_{0}^{1} (2 x - 3) d x

d er i v a t i v e f (x) = \frac{x ^{3} + 2 x + 7}{x ^{2} - 5}

\int_{1}^{1.5} \frac{2}{5} (x + 1) d x

d er i v a t i v e f (t) = 6 t^{3} - 54 t^{2} + 70