GATE 2024 AG – Question 12
Find the Laplace transform of $f(t)=t^4$.
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Correct answer: (B) $24/s^5$
Explanation
For nonnegative integer n,$\mathcal L\{t^n\}=n!/s^{n+1}$ for s>0. Setn=4 to get $4!/s^5=24/s^5$,**B**. The exponent is one greater than the original power because the integration supplies an additional factor1/s.