Project ForgeEngineering Mathematics
Differential Equations
GATE 2012
Medium
If a is a constant, then the value of the integral a²∫₀^∞ xe^(−ax)dx is
- A1/a
- Ba
- 1
- D0
Explanation
∫₀^∞ x·e^(−ax)dx is exactly the Laplace transform of f(t)=t evaluated at s=a, L{t}=1/s², so the integral equals 1/a². Multiplying by a² gives exactly 1.
Source: GATE CH 2012 (2012)
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