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Verify that the Divergence Theorem is true for the vector field F on the region E. Give the flux. F(x, y, z) = 5xi + xyj + 5xzk, E is the cube bounded by the planes x = 0, x = 1, y = 0, y = 2, z = 0, and z = 2. Verify that the Divergence Theorem is true for the vector field F on the region E. F(x, y, z) = (z, y, x), E is the solid ball x2 + y2 + z2 36

Explanation / Answer

divergence theorem

:

F.ds=div F*dv

div F=5+x+5*x=6*x+5

volume integral=(6*x+5)*dx*dy*dz

with x=0 to x=2

y=0 to y=2

z=0 to z=2

answer:88

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