Evaluate the closed-loop line integral oint_C vec F cdot dvec l for the vector field vec F = (x + 2y)hat e _x + (2x + 4y)hat e _y.

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ETAG Engineering Mathematics QUESTION #3771

Question 1

Evaluate the closed-loop line integral $\oint_C \vec{F} \cdot d\vec{l}$ for the vector field $\vec{F} = (x + 2y)\hat{e}_x + (2x + 4y)\hat{e}_y$.

Correct Answer Explanation

The curl of the field is zero, making it a conservative field; thus, any closed-loop integral is zero.