I tried a lot but it gets ugly really soon, any help will be greatly appreciated.
T hanks
2026-04-01 20:25:41.1775075141
Use divergence theorem to find $\iint_S (2x+2y+z^2) dS$ Where $S$ is the sphere $ x^2+y^2+z^2 = 1$
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The divergence theorem is: $$\iint_{\text{Surface of volume}} (\mathbf F \cdot \mathbf n)dS = \iiint_{\text{Volume}} (\text{div }\mathbf F)dV$$
On the unit sphere we have $\mathbf n = (x,y,z)$.
Find a suitable $\mathbf F$ and substitute it in the formula.