Q5.(a) Verify Stokes Theorem for the vector field F(x, y, z) = -z)i + 3xyj+ 5zkby evaluating the line integral and the surface integral where o is theportion of the paraboloid z = 16 -x - y above the xy-plane. Assume thatthe surface has an upward orientation.(b) Use spherical coordinates to find the volume of the solid within the spherex +y +z = 16, outside the cone z =x +y', and above the xy-plane.

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Answered: Verify Stokes Theorem for the vector…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.