Laplace変換・逆変換　Laplace変換の例5

Laplace変換・逆変換 電験 理論

定積分のLaplace変換

\displaystyle{\mathcal{L}\left[ \int_0^t f(x)dx \right] = \int_0^\infty \left( \int_0^t f(x)dx \right) \exp(-st)dt }

\displaystyle{ = \left[ \int_0^t f(x)dx \left( - \frac{1}{s}\exp(-st) \right) \right]_0^\infty - \int_0^\infty f(t) \left( - \frac{1}{s} \exp(-st)\right) dt }

\displaystyle{= \frac{1}{s} \int_0^\infty f(t)\exp(-st) dt = \frac{F(s)}{s} }