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## Homework Statement

Griffiths Introduction to Electrodynamics 4th Edition

Example 1.10

Check the divergence theorem using the function:

v = y^2 (i) + (2xy + z^2) (j) + (2yz) (k)

and a unit cube at the origin.

## Homework Equations

(closed)∫v⋅da = ∫∇⋅vdV

The flux of vector v at the boundary of the closed surface (surface integrals) is equal to the volume integral of the divergence of the vector field.

## The Attempt at a Solution

I have completed the volume integral of ∇⋅v and it equals 2. However the issue I am running into is that I do not understand how to properly construct all 6 of the surface integrals necessary to determine the left hand side of the equation. Obviously it must equal 2 but I need help setting up the integrals.

This is an example problem in the Griffiths E&M text however it just shows the integrals and their solutions rather than how each integral is conceived for each surface of the cube.

If anyone can give me a walkthrough on how to set up those integrals, I would appreciate it immensely.

Thank you.