Question

Calculate the Green’s value for the functions F = y^2 and G = x^2 for the region x = 1 and y = 2 from origin.

(a) 0

(b) 2

(c) -2

(d) 1

I got this question during an interview for a job.

This key question is from Green’s Theorem topic in division Vector Calculus of Electromagnetic Theory

Answer 1

The correct choice is (c) -2

For explanation I would say: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(2x – 2y)dx dy. On integrating for x = 0->1 and y = 0->2, we get Green’s value as -2.