Verify Stokes Theorem for the vector field F(x, y, z) = (y-z)i + 3xy j + 5zk by evaluating the line integral and the surface integral where is the portion of the paraboloid z = 16 - x - y above the xy-plane. Assume that the surface has an upward orientation.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q5.(a) Verify Stokes Theorem for the vector field F(x, y, z) = -z)i + 3xyj+ 5zk
by evaluating the line integral and the surface integral where o is the
portion of the paraboloid z = 16 -x - y above the xy-plane. Assume that
the surface has an upward orientation.
(b) Use spherical coordinates to find the volume of the solid within the sphere
x +y +z = 16, outside the cone z =x +y', and above the xy-plane.
Transcribed Image Text:Q5.(a) Verify Stokes Theorem for the vector field F(x, y, z) = -z)i + 3xyj+ 5zk by evaluating the line integral and the surface integral where o is the portion of the paraboloid z = 16 -x - y above the xy-plane. Assume that the surface has an upward orientation. (b) Use spherical coordinates to find the volume of the solid within the sphere x +y +z = 16, outside the cone z =x +y', and above the xy-plane.
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