Given V⃗ = x cos² y î + x²eᶻ ĵ + z sin² y k̂ and S the surface of a unit cube…

GATE · 1993 · CS · Question 2 subpartsModified — slightly modified from the official paper; see the solution

Given V⃗ = x cos² y î + x²eᶻ ĵ + z sin² y k̂ and S the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of integral ∬ₛ V⃗·n̂ dS is ______

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