The Laplace transform F(x) of a function f (t ) is given by the formula. $F ( x ) = \int _ { 0 } ^ { + \infty } f ( t ) e ^ { - x t } \mathrm {~d} t$
Find $F ( x )$ if $f ( t ) = 8$ .

A) $\frac { 1 } { 8 x }$
B) $\frac { 8 } { x ^ { 2 } }$
C) $\frac { x } { 8 }$
D) $- \frac { x } { 8 }$
E) $\frac { 8 } { x }$

Question

The Laplace transform F(x) of a function  f (t ) is given by the formula.   $F ( x ) = \int _ { 0 } ^ { + \infty } f ( t ) e ^ { - x t } \mathrm {~d} t$  
Find $F ( x )$ if $f ( t ) = 8$ .

A) $\frac { 1 } { 8 x }$
B) $\frac { 8 } { x ^ { 2 } }$
C) $\frac { x } { 8 }$
D) $- \frac { x } { 8 }$
E) $\frac { 8 } { x }$

Quizplus · Accepted Answer

Given $f(t) = 8$, the Laplace transform $F(x)$ is calculated as $F(x) = \int_{0}^{+\infty} 8e^{-xt} dt$. Solving this integral yields $F(x) = \frac{8}{x}$, which matches option E.

The Laplace Transform F(x) of a Function F (T F(x)=∫0+∞f(t)e−xt dtF ( x ) = \int _ { 0 } ^ { + \infty } f ( t ) e ^ { - x t } \mathrm {~d} tF(x)=∫0+∞​f(t)e−xt dt

The Laplace Transform F(x) of a Function F (T $F ( x ) = \int _ { 0 } ^ { + \infty } f ( t ) e ^ { - x t } \mathrm {~d} t$