I'll keep the improper integral with us the whole time.
An improper integral occurs when one or more of these conditions is not satisfied.
So that's the improper integral from 0 to infinity of e to the minus st times 1 here.
Eso es la integral impropia desde 0 hasta el infinito de e para el st menos veces 1 aquí.
limit to infinity and it doesn't come to a finite number, the limit doesn't approach anything, that means that k the improper integral diverges.
límite hasta el infinito y no llegan a un finito número, el límite de no acercarse a nada, eso significa que k la integral impropia diverge.
So the Laplace transform of some function of t is equal to the improper integral from 0 to infinity of e to the minus st times our function.
Por lo que es igual a la transformada de Laplace de algunas funciones de t la integral impropia de 0 a infinito e negativo St veces nuestra función.
Well, our definition of the Laplace transform, that says that it's the improper integral.
Pues bien, nuestra definición de la transformada de Laplace, dice que es la integral impropia.
The improper integral from 0 to infinity of e to the minus st times f of t - so whatever's between the Laplace
La integral impropia de 0 a infinito e negativo St veces f de t - así sea entre el Laplace
The Laplace Transform for our purposes is defined as the improper integral.
La transformada de Laplace para nuestros propósitos se define como la integral impropia.
Thus this is a doubly improper integral.
Because the t's are involved in evaluating the boundaries, since we're doing our definite integral or improper integral.
Porque la an está involucrados en la evaluación de los límites, ya estamos haciendo nuestra integral definida o integral impropia.
And when you do the integration by parts, this could be an indefinite integral, an improper integral, a definite integral, whatever.
So anyway, let's take the anti-derivative and evaluate this improper definite integral, or this improper integral.
Así que de todos modos, vamos a tomar la primitiva y evaluar Esta integral definida inadecuada, o Esta integral impropia.
Thus this is a doubly improper integral.
Así, esta es una integral doblemente impropia.