Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stakes’ Theorem to determine the value of the surface integral ∬ S ( ∇ × F ) ⋅ n d S . Assume that n points in an upward direction. 19. F = 〈2 y – z, x – y – z 〉; S is the cap of the sphere (excluding its base) x 2 + y 2 + z 2 = 25, for 3 ≤ x ≤ 5.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stakes’ Theorem to determine the value of the surface integral ∬ S ( ∇ × F ) ⋅ n d S . Assume that n points in an upward direction. 19. F = 〈2 y – z, x – y – z 〉; S is the cap of the sphere (excluding its base) x 2 + y 2 + z 2 = 25, for 3 ≤ x ≤ 5.
Stokes’ Theorem for evaluating surface integralsEvaluate the line integral in Stakes’ Theorem to determine the value of the surface integral
∬
S
(
∇
×
F
)
⋅
n
d
S
. Assume thatnpoints in an upward direction.
19.F = 〈2y – z, x – y – z〉; S is the cap of the sphere (excluding its base) x2 + y2 + z2 = 25, for 3 ≤ x ≤ 5.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stokes’ Theorem to determine the value of the surface integral ∫∫S (∇ x F) ⋅ n dS. Assume n points in an upward direction.
F = ⟨4x, -8z, 4y⟩; S is the part of the paraboloidz = 1 - 2x2 - 3y2 that lies within the paraboloid z = 2x2 + y2 .
Describe and sketch the surface given by the function.
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