0 0 votes Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}$ denote the unit vectors along the $x – $axis and the $y – $axis, respectively. A contour $\text{C}$ in the $x – y$ plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral $$ \oint_{c}\overrightarrow{\rm F}(x, y) \cdot (dx \overrightarrow{i} + dy \overrightarrow{j}) $$ is _______________. $0$ $1$ $8 + 2 \pi$ $ – 1$ Vector Analysis gateece-2022 vector-analysis complex-analysis + – Arjun 941 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
