Question

If the exit age distribution is given as δ(t – 4), then \(\int_0^∞\) t^2 E(t)dt is ____

(a) 16

(b) 4

(c) 8

(d) 20

I got this question by my college professor while I was bunking the class.

My doubt stems from Non Ideal Flow Basics in portion Fluid-Fluid Reactions: Kinetics & Basics of Non Ideal Flow of Chemical Reaction Engineering

Answer 1

The correct option is (a) 16

To explain: Exit age distribution is represented by dirac delta function. \(\int_0^∞\) δ(t-τ)f(t)dt = f(τ). Hence, \(\int_0^∞\) t^2 E(t)dt = 42 = 16.