Chapter 16.9, Problem 8E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use the Divergence Theorem to calculate the surface integral ∫∫_{s}**F** · *d*S; that is, calculate the flux of **F** across *S.*

**8. F**(*x, y, z*) = (*x*^{3} + *y*^{3}) **i** + (*y*^{3} + *z*^{3}) **j** + (*z*^{3} + *x*^{3}) **k**, *S* is the sphere with center the origin and radius 2

To determine

**To calculate:** The flux of vector field

Explanation

**Given data:**

The vector field is

The 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 spherical coordinate system.

Here,

**Calculation of**
**:**

Substitute

**Calculation of flux of vector field:**

Substitute

Parameterize the sphere with radius

Substitute

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