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. 18. F = r /| r |; S is the paraboloid x = 9 – y 2 – z 2 for 0 ≤ x ≤ 9 (excluding its base), where r = 〈 x , y , z 〉.
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. 18. F = r /| r |; S is the paraboloid x = 9 – y 2 – z 2 for 0 ≤ x ≤ 9 (excluding its base), where r = 〈 x , y , z 〉.
Solution Summary: The author explains Stokes' Theorem: Let S be an oriented surface in R3 with a piecewise-smooth closed boundary C whose orientation is consistent with that of S
Stokes’ Theorem for evaluating surface integralsEvaluate the line integral in Stakes’ Theorem to determine the value of the surface integral
∬
S
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∇
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. Assume thatnpoints in an upward direction.
18.F = r/|r|; S is the paraboloid x = 9 – y2 – z2 for 0 ≤ x ≤ 9 (excluding its base), where r = 〈x, y, z〉.
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.
Find the surface area of the "Coolio McSchoolio" surface shown below using the formula:
SA = integral, integral D, ||ru * rv||dA
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The parameterization of the surface is:
r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1
A.) (pi/3)(6squareroot(6) - 8)
B.) (pi/3)(6squareroot(6) - 2squareroot(2))
C.) (pi/6)(2squareroot(3) - squareroot(2))
D.) (pi/6)(squareroot(6) - squareroot(2))
E.) (5pi/6)(6 - squareroot(2))
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
University Calculus: Early Transcendentals (4th Edition)
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