Allied & ICAR Exam Bank • ALLIED_2717 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

According to the First Shifting Theorem, if $\mathcal{L}\{f(t)\} = F(s)$, then $\mathcal{L}\{e^{a t} f(t)\}$ equals:

Options:

  • (A) $F(s - a)$
  • (B) $F(s + a)$
  • (C) $e^{-as} F(s)$
  • (D) $\frac{1}{s} F(s)$

Answer Key:

A

Step-by-Step Solution & Explanation

First shifting property: $\int_0^\infty e^{-st} e^{at} f(t) dt = \int_0^\infty e^{-(s-a)t} f(t) dt = F(s - a)$.
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