Allied & ICAR Exam Bank • ALLIED_0784NAT • 2 Marks
Section 1: Engineering Mathematics
Vector Calculus
Subtopic: Stokes, Gauss and Green's theorems
Question Statement:
Using Green's Theorem, the area $A$ enclosed by a simple closed curve $C$ in the $xy$-plane is given by $A = \frac{1}{2} \oint_C (x dy - y dx)$. For an ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ ($a = 4, b = 3$), the enclosed area $A = \pi a b = 12\pi$. The value of $A / \pi$ is:
Answer Key:
12
Step-by-Step Solution & Explanation
Area of ellipse is $\pi a b = \pi \times 4 \times 3 = 12\pi$. Thus $A / \pi = 12$.