**N**dA

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

*+x^2y*

**i***+y^2z*

**j**

**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)

*+9sin^2(theta)cos(phi)*

**i***+9cos(theta)sin(theta)*

**j**

**k**and

F=27sin(θ)cos^2(θ)cos(φ)

*+27sin^3(θ)cos^2(φ)sin(φ)*

**i***+27sin^2(θ)cos(θ)sin^2(φ)*

**j**

**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!