Question

Which of the following is not a property of double integration?

(a) ∬ af(x,y)ds = a∬ f(x,y)ds, where a is a constant

(b) ∬ (f(x,y)+g(x,y))ds = ∬f(x,y)ds+ ∬g(x,y)ds

(c) \(∬_0^Df(x,y)ds = ∬_0^{D1}f(x,y)ds+ ∬_{D1}^{D2}f(x,y)ds,\) where D is union of disjoint domains D1 and D2

(d) ∬(f(x,y)*g(x,y))ds = ∬f(x,y)ds*∬g(x,y)ds

I had been asked this question during an interview.

My question is based upon Change of Order of Integration: Double Integral topic in portion Multiple Integrals of Engineering Mathematics

Answer 1

Correct answer is (d) ∬(f(x,y)*g(x,y))ds = ∬f(x,y)ds*∬g(x,y)ds

The best explanation: The following are the properties of double integration:

∬af(x,y)ds = a∬f(x,y)ds

 ∬f(x,y)+g(x,y))ds = ∬f(x,y)ds+ ∬g(x,y)ds

 \(∬_0^Df(x,y)ds = ∬_0^{D1}f(x,y)ds+ ∬_{D1}^{D2}f(x,y)ds\)