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. 24. F = 〈 e x , 1 / z , y 〉 ; S is the part of the surface z = 4 − 3 y 2 that lies within the paraboloid z = x 2 + y 2 .
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. 24. F = 〈 e x , 1 / z , y 〉 ; S is the part of the surface z = 4 − 3 y 2 that lies within the paraboloid z = x 2 + y 2 .
Solution Summary: The author evaluates the surface integral by obtaining line integral in Stokes' theorem, where n is the unit vector normal to S determined by its orientation.
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.
24.
F
=
〈
e
x
,
1
/
z
,
y
〉
; S is the part of the surface z = 4 − 3y2 that lies within the paraboloid z = x2 + y2.
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
What is a unit normal to the surface x?y + 2xz = 4 at the point (2, –2, 3)
O+3+歌
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.