Allied & ICAR Exam Bank • ALLIED_2714 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Laplace transforms and their inverse

Question Statement:

The Laplace transform of $f(t) = t^3$ is $\frac{k}{s^4}$. The integer $k$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

$\mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}}$. For $n = 3$, $3! = 6$. So $k = 6$.
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