GATE 2026 MT – Question 11

Engineering Mathematics · Differential equations · 1 mark · Multiple choice

Given $f(t)=e^{-at}$, where $a$ is a constant, its Laplace transform is $\mathcal L[f(t)]=F(s)$. Which one of the following options is correct?

$F(s)=\frac1{s-a}$
$F(s)=\frac{s}{s^2-a^2}$
$F(s)=\frac{a}{s^2-a^2}$
$F(s)=\frac1{s+a}$

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Correct answer: (D) $F(s)=\frac1{s+a}$

Explanation

By definition, $F(s)=\int_0^\infty e^{-at}e^{-st}\,dt=\int_0^\infty e^{-(s+a)t}\,dt$.

For $\operatorname{Re}(s+a)>0$, the upper-limit term vanishes, giving $F(s)=1/(s+a)$. The correct option is **D**.