Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.6 Stokes’ Theorem and the Curl of F, #30 · Multivariable Calculus · Green, Stokes & divergence

### 31–34 compute … over the top half of the sphere …

True or false: when two vector fields have the same curl at all points: (a) their difference is a constant field (b) their difference is a gradient field (c) they have the same divergence.

### 31–34
compute $\iint curl F \cdot n d S$ over the top half of the sphere $x^{2} + y^{2} + z^{2} = 1$ and (separately) $\oint_{C} F \cdot d R$ around the equator.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.6 Stokes’ Theorem and the Curl of F, #30

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