Question

What is the area under a doublet function?

(a) Unity

(b) Negative

(c) Zero

(d) Positive

The question was posed to me in a dream while sleeping

The origin of the question is The Impulse Function in portion Signals and Systems Basics of Signals and Systems

Answer 1

Right choice is (c) Zero

Easy explanation: We can explain by-

Integration -infinity to +infinity x(t)∂’(t)dt= negative of Integration -infinity to +infinity x’(t)∂’(t)dt=-x’(t)|t=0=-X’(0), where x(t) is any continuous function having a continuous derivative at t=0. This is ∫∂’(t)=0.