?In Exercises 1 - 6, verify the Divergence Theorem by evaluating \(\int_{S} \int \mathrm{F} \cdot \mathrm{N} d S\) as a surface inte

Chapter 15, Problem 4

(choose chapter or problem)

In Exercises 1 - 6, verify the Divergence Theorem by evaluating

\(\int_{S} \int \mathrm{F} \cdot \mathrm{N} d S\)

as a surface integral and as a triple integral.

\(\mathbf{F}(x, y, z)=x y \mathbf{i}+z \mathbf{j}+(x+y) \mathbf{k}\)

S: surface bounded by the planes y = 4 and z = 4 - x and the coordinate planes

Text Transcription:

int_S int F cdot N dS

F(x, y, z) = xyi + zj + (x + y)k

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