Volume For the vector field verify the following integral, where is the volume of the

Chapter 15, Problem 25

(choose chapter or problem)

For the vector field \(\mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k}\), verify the following integral, where V is the volume of the solid bounded by the closed surface S.

\(\int_{S} \int \mathbf{F} \cdot \mathbf{N} d S=3 V\)

Text Transcription:

F(x, y, z) = xi + yj + zk

int_S int F cdot N dS = 3V

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