GATE 2021 MA – Question 26

Calculus · Vector Calculus · 1 mark · Numerical answer

Γ is the counterclockwise boundary of the square with vertices (0,0),(2,0),(2,2),(0,2). Evaluate ∮_Γ(1−y²)dx+xdy.

Show answer and explanation

Correct answer: 12 to 12

Explanation

Green’s theorem gives ∫₀²∫₀²[∂x(x)−∂y(1−y²)]dydx=∫₀²∫₀²(1+2y)dydx=2(2+4)=**12**.

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