Word Count : 266

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We will use Gauss' theorem (Divergence theorem) to compute the flux of the vector field \(\vec{A} = x^3 \hat{i} + x^2z \hat{j} + yz \hat{k}\) through the surface of a cube of side 2 units. ### Step 1: Gauss' Theorem Gauss' theorem states: \[ \oint_{S} \vec{A} \cdot d\vec{S} = \iiint_{V} (\nabla \cdot \vec{A}) \, dV \] This means that the total flux through the surface \(S\) _______ _____ ______ __________ ______ __________ ___ ________ ________.
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