Allied & ICAR Exam Bank • ALLIED_1021 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Stokes' theorem

Question Statement:

Stokes' Theorem relates which of the following two integrals?

Options:

  • (A) A line integral around a closed curve to a surface integral over an open surface bounded by that curve
  • (B) A surface integral over a closed surface to a volume integral
  • (C) A line integral along an open curve to a double integral
  • (D) A volume integral to a contour integral

Answer Key:

A

Step-by-Step Solution & Explanation

Stokes' theorem states that $\oint_C \vec{F} \cdot d\vec{r} = \iint_S (\nabla \times \vec{F}) \cdot d\vec{S}$, which connects the circulation of a vector field along closed boundary $C$ to the flux of its curl across surface $S$.
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