Project ForgeEngineering Mathematics
Calculus
GATE 2012
Medium
The inverse Laplace transform of the function F(s) = 1/(s(s+1)) is given by
- Af(t)=sin t
- Bf(t)=e⁻ᵗ sin t
- Cf(t)=e⁻ᵗ
- f(t)=1−e⁻ᵗ
Explanation
Partial fractions: 1/(s(s+1)) = 1/s − 1/(s+1). Taking the inverse Laplace transform of each term: L⁻¹{1/s}=1 and L⁻¹{1/(s+1)}=e⁻ᵗ, so f(t)=1−e⁻ᵗ.
Source: GATE ME 2012 (Booklet Code A) (2012)
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