?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 5

(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.

\(\mathbf{F}(x, y, z)=x z \mathbf{i}+z y \mathbf{j}+2 z^{2} \mathbf{k}\)

S: surface bounded by \(z=1-x^{2}-y^{2}\) and z = 0

Text Transcription:

int_S int F cdot N dS

F(x, y, z) = xzi + zyj + 2z^{2}k

z = 1 - x^2 - y^2

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