Let be the closed surface consisting of the portion of theparaboloid z = x2 + y2 for

Chapter 15, Problem 22

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Let σ be the closed surface consisting of the portion of the paraboloid \(z=x^{2}+y^{2}\) for which \(0 \leq z \leq 1\) and capped by the disk \(x^{2}+y^{2} \leq 1\) in the plane \(z = 1\). Find the flux of the vector field \(F(x, y, z) = z j − yk\) in the outward direction across \(\sigma\).

Equation Transcription:

0 ≤ z ≤ 1

x2 + y2 ≤ 1

σ

Text Transcription:

z = x^2+ y^2

0 <= z <= 1

x^2 + y^2 <= 1

z = 1

F(x, y, z) = z j − yk

sigma