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**HeheZz** Verify Gauss Divergence Theorem ∭∇.F dxdydz=∬F. **N**dA

Where the closed surface S is the sphere x^2+y^2+z^2=9 and the vector field F = xz^2**i**+x^2y**j**+y^2z**k**

I have tried to solve the left hand side which appear to be (972*pi)/5

However, I cant seems to solve the right hand side to get the same answer.

I substitute x = 3sin(theta)cos(phi), y=3sin(theta)sin(phi), z=3cos(theta)

Therefore **N**=9sin^2(theta)cos(phi)**i**+9sin^2(theta)cos(phi)**j**+9cos(theta)sin(theta)**k**

and

F=27sin(θ)cos^2(θ)cos(φ)**i**+27sin^3(θ)cos^2(φ)sin(φ)**j**+27sin^2(θ)cos(θ)sin^2(φ)**k**

then I used ∫(0-2pi)∫(0-pi) F. **N** dθdφ

I got the final answer as (324*pi)/5 which does not match with left hand side.

Hope anyone can help here plz. Thanks!