GATE 2025 ES – Question 11
For $s>|a|$,find the Laplace transform of $f(x)=\cosh ax$.
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Correct answer: (C) $s/(s^2-a^2)$
Explanation
Write $\cosh ax=(e^{ax}+e^{-ax})/2$. Integrating each exponential against $e^{-sx}$ gives $\frac12[1/(s-a)+1/(s+a)]=s/(s^2-a^2)$. The condition $s>|a|$ ensures both integrals converge. Hence **C**.