   Chapter 16.9, Problem 9E

Chapter
Section
Textbook Problem

Use the Divergence Theorem to calculate the surface integral ∫∫s F · dS; that is, calculate the flux of F across S.9. F(x, y, z) = xey i + (z - ey) j - xy k, S is the ellipsoid x2 + 2y2 + 3z2 = 4

To determine

To calculate: The flux of vector field F(x,y,z)=xeyi+(zey)jxyk across the surface of the solid S which is ellipsoid x2+2y2+3z2=4 .

Explanation

Given data:

The vector field is F(x,y,z)=xeyi+(zey)jxyk .

The surface S is a ellipsoid x2+2y2+3z2=4 .

Formula used:

Write the expression to find flux of the vector field F(x,y,z) across the surface S .

SFdS=EdivFdV (1)

Here,

E is the solid region.

Write the expression to find divergence of vector field F(x,y,z)=Pi+Qj+Rk .

divF=xP+yQ+zR (2)

Calculation of divF :

Substitute xey for P , (zey) for Q , and (xy) for R in equation (2),

divF="

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