Please work this out with a picture attached with your work by hand, I will give

Question

Please work this out with a picture attached with your work by hand, I will give a great rating if you are full in your steps and write legibally :D, many, many, many thanks for the help. Verify gauss' theorem (evaluate dirececly both sides of stokes theorem equation for the vector V = (xy xhat) + (yz yhat) + (z^2 zhat) over the unit cube with vertices at (0,0,0) , (1,0,0) , (1,1,0) , (0,1,0) , (0,0,1) , (1,0,1) , (1,1,1) and (0,1,1). HINT - the hint says to verify this by evaluating each side of gauss's theorem involving one side with the surface integral and the other with the volume integral

Explanation / Answer

To calculate this, we need only the component of in the direction, since the other two components measure flow parallel to the plane and do not cross the plane, so can

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