Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C where C is in the direction of positive orientation (that is, counterclockwise when looking down from the positive z-axis): f..F. F. dr = J (cu (curl F). n ds where F(x, y, z) = xyi + x²j + z²k and C is the intersection of the paraboloid z = x² + . and the 6 plane z = y. #11 i

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C where C is in the direction of
positive orientation (that is, counterclockwise when looking down from the positive z-axis):
fo
F. dr =
(c
(curl F). n ds where F(x, y, z) = xyi + x²j + z²k and C is the intersection of the paraboloid z = x² + y² and the
plane z = y.
#11
i
0
Transcribed Image Text:Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C where C is in the direction of positive orientation (that is, counterclockwise when looking down from the positive z-axis): fo F. dr = (c (curl F). n ds where F(x, y, z) = xyi + x²j + z²k and C is the intersection of the paraboloid z = x² + y² and the plane z = y. #11 i 0
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