State the Divergence Theorem $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V$

question 16

Multiple Choice

State the Divergence Theorem.

• A)If W is a solid region whose boundary S is a piecewise smooth surface, then \(\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V\)
• B)If W is a solid region whose boundary S is a smooth surface oriented outward, then \(\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V\)
• C)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, and if \(\vec { F }\) is a smooth vector field on an open region containing W and S, then
• \(\int_{S} \vec{F} \cdot \overrightarrow{d A}=\int_{W} \operatorname{div} \vec{F} d V\)
• D)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, then \(\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W } { div } \vec { F } \cdot \overrightarrow { d \bar { V } }\)
• E)If S is a solid region whose boundary W is a piecewise smooth surface oriented outward, then \(\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W } { div } \vec { F } { d { V } }\)

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Definitions:

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An irregularity or deviation from what is standard, normal, or expected.

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