Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 3 i + x 2 y j + x y k ; σ is the surface of the solid bounded by z = 4 − x 2 , y + z = 5 , z = 0 and y = 0.
Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. F x , y , z = x 3 i + x 2 y j + x y k ; σ is the surface of the solid bounded by z = 4 − x 2 , y + z = 5 , z = 0 and y = 0.
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.
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. (note: do not use gauss' theorem)
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
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