For f(t)=42t+6e-8t, find F(s)= 0 f(t)e-st\,dt.

GATE 2020 AG – Question 37

Engineering Mathematics · Differential Equations · 2 marks · MTA

For $f(t)=4\cos2t+6e^{-8t}$, find $F(s)=\int_0^\infty f(t)e^{-st}\,dt$.

$4s/(s^2+4)+6/(s+8)$
$4s/(s^2-4)+6/(s-8)$
$8/(s^2+4)+6/(s+8)$
$8/(s^2-4)+6/(s-8)$

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Correct answer: MTA

Explanation

Linearity and standard transforms give L{cos2t}=s/(s²+4) and L{e^(−8t)}=1/(s+8), so the mathematical expression is A. The appended final key marks this question MTA (marks to all); that grading is retained with all four original choices.

GATE 2020 AG – Question 37

Explanation

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