Allied & ICAR Exam Bank • ALLIED_2693NAT • 2 Marks
Section 1: Engineering Mathematics
Vector Calculus
Subtopic: Stokes, Gauss and Green's theorems
Question Statement:
By Green's theorem, the area of a closed planar region $D$ bounded by $C$ is given by $\frac{1}{2} \oint_C (x dy - y dx)$. For an ellipse with semi-axes $a = 4, b = 3$, the value of $\frac{1}{2} \oint_C (x dy - y dx)$ is $k \pi$. The integer $k$ is:
Answer Key:
12
Step-by-Step Solution & Explanation
The area of an ellipse is $\pi a b = \pi (4)(3) = 12\pi$. Hence $k = 12$.