Let be the surface of the cube bounded by the planesx = 1, y = 1, z = 1, oriented by

Chapter 15, Problem 21

(choose chapter or problem)

Let σ be the surface of the cube bounded by the planes \(x=\pm 1, y=\pm 1, z=\pm 1\) , oriented by outward unit normals. In each part, find the flux of \(F\) across \(\sigma\).

(a) \(F(x, y, z) = xi\)

(b) \(F(x, y, z) = xi + y j + zk\)

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

Equation Transcription:

σ

x = ±1, y = ±1, z = ±1

Text Transcription:

σ

x = pm 1, y = pm 1, z = pm 1

F(x, y, z) = xi

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

F(x, y, z) = x^2i + y^2j + z^2k