Stokes’ Theorem for surface integrals Use Stokes’ Theorem to evaluate the surface integral ∬ S ( ∇ × F ) ⋅ n d S . Assume that n is the outward normal. 60. F = 〈 x 2 – z 2 , y 2 , xz 〉, where S is the hemisphere x 2 + y 2 + z 2 = 4, for y ≥ 0
Stokes’ Theorem for surface integrals Use Stokes’ Theorem to evaluate the surface integral ∬ S ( ∇ × F ) ⋅ n d S . Assume that n is the outward normal. 60. F = 〈 x 2 – z 2 , y 2 , xz 〉, where S is the hemisphere x 2 + y 2 + z 2 = 4, for y ≥ 0
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 surface integralsUse Stokes’ Theorem to evaluate the surface integral
∬
S
(
∇
×
F
)
⋅
n
d
S
. Assume thatnis the outward normal.
60. F = 〈x2 – z2, y2, xz〉, where S is the hemisphere x2 + y2 + z2 = 4, for y ≥ 0
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.
What is a unit normal to the surface x?y + 2xz = 4 at the point (2, –2, 3)
O+3+歌
Evaluate the surface integral.
J y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u sin(v), v), 0sus 6,0 SV SR.
[(10) ()-1]
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lus III
1Unit
Use Stokes's Theorem to evaluate
F. dr where C is oriented counterclockwise as viewed
from above, F(x, y, z) =, C is the circle x2 + y? = 4, and z = 4.
Chapter 17 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
Thomas' Calculus: Early Transcendentals (14th Edition)
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