Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral ∬ s ( ∇ × F ) ∙ n dS . Assume n points in an upward direction. 21 . F = 〈 y , z − x , − y 〉 ; S is the part of the paraboloid z = 2 − x 2 − 2 y 2 that lies within the cylinder x 2 +y 2 =1.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral ∬ s ( ∇ × F ) ∙ n dS . Assume n points in an upward direction. 21 . F = 〈 y , z − x , − y 〉 ; S is the part of the paraboloid z = 2 − x 2 − 2 y 2 that lies within the cylinder x 2 +y 2 =1.
Solution Summary: The author evaluates the surface integral value by obtaining line integral in Stokes' theorem.
Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in stokes’ Theorem to determine the value of the surface integral
∬
s
(
∇
×
F
)
∙ndS. Assume n points in an upward direction.
21. F =
〈
y
,
z
−
x
,
−
y
〉
;
S is the part of the paraboloid z = 2 − x2 − 2y2 that lies within the cylinder x2+y2=1.
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 .
Verify Stokes' theorem. Assume that the surface S is oriented upward. F=3zi−5xj+2yk; S that portion of the paraboloid z=36−x^2−y^2 for z≥0 I'm having trouble finding the normal n*dS in Stokes's Theorem
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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