GATE 2018 ME (ME1) – Question 48
F(s) is the Laplace transform of $f(t)=2t^2e^{-t}$. F(1), to two decimals, is ______.
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Correct answer: 0.48 to 0.52
Explanation
Use the transform of $t^2$ and exponential shift: $F(s)=4/(s+1)^3$. Therefore $F(1)=4/8=0.50$. Both the initial factor 2 and the factorial 2 contribute.