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18.5: A.5- Derivación de la Transformación de Laplace de la Integral de Convolución
https://espanol.libretexts.org/Ingenieria/Introduccion_a_los_Sistemas_Dinamicos_Lineales_Invariantes_en_el_Tiempo_para_Estudiantes_de_Ingenieria_(Hallauer)/18%3A_Ap%C3%A9ndice_A-_Tabla_y_Derivaciones_de_Pares_Transformada_de_Laplace/18.05%3A_A.5-_Derivaci%C3%B3n_de_la_Transformaci%C3%B3n_de_Laplace_de_la_Integral_de_Convoluci%C3%B3n
$C I(t)=\int_{\tau=0}^{\tau=t} f_{1}(\tau) f_{2}(t-\tau) d \tau=\int_{\tau=0}^{\tau=t} f_{1}(t-\tau) f_{2}(\tau) d \tau\label{eqn:6.1}$ \[C I(t)=\int_{\tau=0}^{\tau=t} f_{1}(\tau) f_{2}(t-\tau) d \... $C I(t)=\int_{\tau=0}^{\tau=t} f_{1}(\tau) f_{2}(t-\tau) d \tau=\int_{\tau=0}^{\tau=t} f_{1}(t-\tau) f_{2}(\tau) d \tau\label{eqn:6.1}$ $C I(t)=\int_{\tau=0}^{\tau=t} f_{1}(\tau) f_{2}(t-\tau) d \tau=\int_{\tau=0}^{\tau=\infty} f_{1}(\tau) f_{2}(t-\tau) d \tau \nonumber$ $L[C I(t)]=L\left[\int_{\tau=0}^{\tau=\infty} f_{1}(\tau) f_{2}(t-\tau) d \tau\right]=\int_{t=0}^{t=\infty} e^{-s t}\left[\int_{\tau=0}^{\tau=\infty} f_{1}(\tau) f_{2}(t-\tau) d \tau\right] d t \nonumber$

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