Use the Divergence Theorem to calculate the surface integral ∫∫S F · dS; that is, calculate the flux of F across S.
F(x,y,z) = x2z3 i + 5xyz3 j + xz4 k
S is the surface of the box with vertices (±1,±2,±2)
Thanks in advance!
F(x,y,z) = x2z3 i + 5xyz3 j + xz4 k
S is the surface of the box with vertices (±1,±2,±2)
Thanks in advance!
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∫∫(S) F · dS = ∫∫∫(V) divF dV ,
V is the volume of the cube (so x goes from -1 to +1, y from -2 to +2 and z from -2 to +2).
divF = 2 x z^3 + 5 x z^3 + 4 x z^3 = 11 x z^3.
Integrate and you should get 0
V is the volume of the cube (so x goes from -1 to +1, y from -2 to +2 and z from -2 to +2).
divF = 2 x z^3 + 5 x z^3 + 4 x z^3 = 11 x z^3.
Integrate and you should get 0