Allied & ICAR Exam Bank • ALLIED_2686 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

Evaluate $\int_C (x dx + y dy)$ along the circle $x^2 + y^2 = 4$ traversed in counterclockwise direction:

Answer Key:

0

Step-by-Step Solution & Explanation

The integrand is an exact differential: $x dx + y dy = d\left(\frac{x^2 + y^2}{2}\right)$. Over any closed path, the integral of an exact differential is zero.
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