JJC/2013/II/Q2 Using Differential Equations to Model the spread of Disease in a town

A researcher is investigating the spread of a certain disease in a town with a population of 3000 people. The researcher suggests that I, the number of people infected by the disease at time t days satisfies the differential equation , where k is a positive constant. (i)         Given that I = 30 when t = 0, […]


(a)Without using a calculator, solve the inequality (b) Deduce the range of values of x that satisfies. Solutions: (a): x≤-6 or 1≤x<3 or x>3                  (b): 0<x≤e-6 or e≤x<e3 or x>e3 (a) (b) lnx ≤ -6               x ≤ e-6   1≤ lnx <3  e≤x<e3  lnx>3  x>e3 […]

Applications of integration

Differentiate y=5x(e3x) with respect to x and hence find ∫x(e3x) dx Solution: 1/3(x)(e3x) – 1/9(e3x) + C Y = 5x e3x dy/dx = 5x(e3x)(3) + 5 e3x dy/dx = 15x(e3x) + 5(e3x) ∫15x(e3x) + 5(e3x) dx = 5x(e3x) ∫15x(e3x) dx + (5(e3x))/3 = 5x(e3x) 15∫x(e3x) dx = 5x(e3x) – 5/3(e3x) ∫x(e3x) dx = 1/3(x)(e3x) – 1/9(e3x) + […]