Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 3 i + y 3 j + z 3 k ; σ is the surface of the cylindrical solid bounded by x 2 + y 2 = 4 , z = 0 , and z = 3.
Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 3 i + y 3 j + z 3 k ; σ is the surface of the cylindrical solid bounded by x 2 + y 2 = 4 , z = 0 , and z = 3.
Determine the flux of F(x, y, z) = < −x2 + x, y, 8x3 − z + 9 > across the surface with an upward orientation. Let the surface be the portion of the paraboloid z = 9 − 4x2 −4y2 on the first octant above the plane z = 1.
Use the Divergence Theorem to find the flux of
F(x, y, z)=z³ i-x³j+y³ k
across the sphere x² + y² + z² = a² with outward orientation.
$ = i
Find the flux of F across the surface σ by expressing σ parametrically.
F(x,y,z)= 3i −7j+zk; σ is the portion of the cylinder x^2 +y^2 =16 between the planes z =−2 and z = 2, oriented by outward unit normals.
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