The Laplace transform of a function f is
A) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { t } f ( t ) d t$
B) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { - t } f ( t ) d t$
C) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { s t } f ( t ) d t$
D) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { - s t } f ( t ) d t$
E) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { s } e ^ { s t } f ( t ) d t$

Question

Quizplus · Accepted Answer

The correct definition of the Laplace transform of a function $f(t)$ involves an integral from 0 to infinity of $e^{-st}f(t)dt$, where $s$ is a complex number parameter.

The Laplace Transform of a Function F Is A) L{f(x)}=∫0∞etf(t)dt\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { t } f ( t ) d tL{f(x)}=∫0∞​etf(t)dt

The Laplace Transform of a Function F Is
A) $\mathcal { L } \{ f ( x ) \} = \int _ { 0 } ^ { \infty } e ^ { t } f ( t ) d t$