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

question 30

Multiple Choice

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 $f ( t ) = e ^ { n t }$ (n constant) .

• A) \(\frac { 1 } { x }\)
• B) \(\frac { 1 } { x - n }\)
• C) \(\frac { n } { x }\)
• D) \(\frac { n } { x - \mathrm { n } }\)
• E) \(n x - n\)

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