Q.39 The Laplace transform of f(t) = 2t + 6 is
- 1 / s + 2 / s2
- 3 / s − 6 / s2
- 6 / s + 2 / s2
- −6 / s + 2 / s2
Laplace Transform of f(t) = 2t + 6
The Laplace transform is an important mathematical technique used to convert
time-domain functions into the frequency domain. Let us evaluate the Laplace
transform of the function:
f(t) = 2t + 6
Important Laplace Transform Formulas
L{1} = 1/s
L{t} = 1/s2
The Laplace transform is linear:
L{a f(t) + b g(t)} = a L{f(t)} + b L{g(t)}
Step-by-Step Solution
Given function:
f(t) = 2t + 6
Applying the Laplace transform:
L{2t + 6} = L{2t} + L{6}
L{2t} = 2 × (1/s2) = 2/s2
L{6} = 6 × (1/s) = 6/s
Therefore,
L{2t + 6} = 6/s + 2/s2
Correct Answer
Option (C): 6/s + 2/s2
Conclusion
The Laplace transform of the function f(t) = 2t + 6 is:
6/s + 2/s2
Understanding linearity and standard Laplace formulas makes such problems
easy to solve in competitive and university examinations.
