GATE 2024 MA – Question 61

Calculus · Vector Calculus · 2 marks · Numerical answer

A C¹ path runs from (0,2) to (3,0). For F(x,y)=(1−2y,1−2x), find ∫F·dr to two decimals.

Show answer and explanation

Correct answer: 0.99 to 1.01

Explanation

F is the gradient of φ=x+y−2xy. Therefore the line integral is endpoint potential difference: φ(3,0)−φ(0,2)=3−2=**1.00**.

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