Consider the line integral \[ _ C ( xdy - ydx ) \] the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

Consider the line integral $$\underset{\text{C}}{\int }\left(\text{xdy}-\text{ydx}\right)$$   the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

Answer: Option A