Stokes’ Theorem for evaluating line integrals Evaluate the line integral ∮ C F ⋅ d r by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation. 15. F = 〈 y 2 , – z 2 , x 〉; C is the circle r ( t ) = 〈3 cos t, 4 cos t , 5 sin t 〉, for 0 ≤ t ≤ 2 p .
Stokes’ Theorem for evaluating line integrals Evaluate the line integral ∮ C F ⋅ d r by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation. 15. F = 〈 y 2 , – z 2 , x 〉; C is the circle r ( t ) = 〈3 cos t, 4 cos t , 5 sin t 〉, for 0 ≤ t ≤ 2 p .
Stokes’ Theorem for evaluating line integralsEvaluate the line integral
∮
C
F
⋅
d
r
by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.
15. F = 〈y2, –z2, x〉; C is the circle r(t) = 〈3 cos t, 4 cos t, 5 sin t〉, for 0 ≤ t ≤ 2p.
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.
Evaluate the line integral ∫CF→⋅dr→ using the Fundamental Theorem of Line Integrals if F→(x,y)=(4x+4y)i→+(4x+4y)j→and Cis the smooth curve from (−1,1)to (5,6).
Enter the exact answer.
∫CF→⋅dr→=
Evaluate the line integral ∮C F ⋅ dr using Stokes’ Theorem. Assume C has counterclockwise orientation.
F = ⟨xz, yz, xy⟩; C is the circle x2 + y2 = 4 in the xy-plane.
Stokes’ Theorem for evaluating line integrals Evaluate theline integral ∮C F ⋅ dr by evaluating the surface integral in Stokes’Theorem with an appropriate choice of S. Assume C has a counterclockwiseorientation.
F = ⟨y2, -z2, x⟩; C is the circle r(t) = ⟨3 cos t, 4 cos t, 5 sin t⟩, for 0 ≤ t ≤ 2π.
University Calculus: Early Transcendentals (3rd Edition)
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