Answer: hi your question is incomplete below is the complete question
Use the Divergence Theorem to calculate the surface integral S F dS with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral
answer : surface integral = 384/5 π
Step-by-step explanation:
Representing the vector field as
F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k
assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.
Hence the divergence will be represented as :
Attached below is the detailed solution
You can see the polygon in the attached figure.
It's a trapezoid, so it's not equilateral, nor regular.
5x + 10x = 180
15x = 180
X = 12
5 x 12 = 60
10 x 12 = 120
The angles are 60° and 120°