Question

The value of $\oint_C x \, dy - y \, dx$, where $C$ is the boundary of the rectangular region formed by $x = 5$, $x = 12$, $y = 0$, and $y = 8$ is:

• A. $56$
• B. $28$
• C. $112$
• D. $72$

Hint:

The line integral $\frac{1}{2} \oint_C (x \, dy - y \, dx)$ is a standard formula for computing the area of a closed region. Therefore, $\oint_C (x \, dy - y \, dx)$ is always equal to $2 \times \text{Area}$.

Answer 1

The Correct Option is C