GATE Electrical Engineering (EE) 2023 Solved Paper

The closed curve shown in the figure is described by
𝑟 = 1 + 𝑐𝑜𝑠 𝜃, where 𝑟 = $\sqrt{{\mathit{x}}^2+{\mathit{y}}^2}$; 𝑥 = 𝑟𝑐𝑜𝑠 𝜃, 𝑦 = 𝑟𝑠𝑖𝑛 𝜃
The magnitude of the line integral of the vector field 𝐹 = −𝑦𝑖̂ + 𝑥𝑗̂around the closed curve is ____________ (Round off to 2 decimal places).