Chapter 16, Problem 39RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find ∬_{S}**F** · **n** *d*S, where **F**(*x*, *y*, *z)* = *x* **i** + *y* **j** + *z* **k** and *S* is the outwardly oriented surface shown in the figure (the boundary surface of a cube with a unit corner cube removed).

To determine

**To find:** The value of
*S* is the outwardly oriented surface.

Explanation

**Given data:**

The vector field is
*S* is the outwardly oriented surface.

**Formula used:**

Write the expression to find flux of the vector field

Here,

Write the expression to find divergence of vector field

Write the expression for volume of cube.

Here,

Find the value of

Substitute

Substitute

Consider the side of full cube is represented by

Consider the side of removed portion of the cube is represented by

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