GATE XE (Engineering Sciences) 2024 - Question 21

Section: Engineering Mathematics | Type: NAT | Marks: 2

Consider the vector field 𝐹⁡⃗⃗⃗ = (2𝑥+ 𝑦2)⁡𝑖̂ + (2𝑥𝑦+ 3𝑦)⁡𝑗̂ and 𝛼𝑚= ∫ 𝐹⁡⃗⃗⃗ 𝐶𝑚 ⋅𝑑𝑟 , 𝑚= 1, 2, where 𝐶1 is an arc of the unit circle connecting the points (1, 0) and (0, 1) and 𝐶2 is the straight line connecting the points (1, 0) and (0, 1). Then, the value (in integer) of 2(𝛼1 2 + 3𝛼2 2) is ______

Answer: 2