Allied & ICAR Exam Bank • ALLIED_0052 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

The work done by the force field $\vec{F} = (2x + y)\hat{i} + x\hat{j}$ in moving a particle from $(0, 0)$ to $(1, 2)$ along the line $y = 2x$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

Along $y = 2x$, $dy = 2 dx$. Work $= \int_0^1 [(2x + 2x) dx + x(2 dx)] = \int_0^1 (4x + 2x) dx = \int_0^1 6x dx = [3x^2]_0^1 = 3$.
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