For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For the vector field
F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk
the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields
==
f F³ · dr = − 18πT.
State Stokes' theorem and then verify Stokes' theorem in this case by
calculating the surface integral over the paraboloid z = 9 (x² + y²)
above the xy-plane.
Transcribed Image Text:For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.
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