Concept explainers
Evaluating a Line
(a).
(b).
Evaluating a Line Integral for Different Parametrizations In Exercises 1–4, show that the value of
(a).
(b).
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Calculus: Early Transcendental Functions (MindTap Course List)
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- Line integrals of vector fields on closed curves Evaluate ∮C F ⋅ dr for the following vector fields and closed oriented curves C by parameterizing C. If the integral is not zero, give an explanation. F = ⟨x, y⟩; C is the circle of radius 4 centered at the origin orientedcounterclockwise.arrow_forwardLine integrals of vector fields on closed curves Evaluate ∮C F ⋅ dr for the following vector fields and closed oriented curves C by parameterizing C. If the integral is not zero, give an explanation. F = ⟨y, x⟩; C is the circle of radius 8 centered at the origin orientedcounterclockwise.arrow_forwardUse Stokes's Theorem to evaluate C F · dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = (cos(y) + y cos(x))i + (sin(x) − x sin(y))j + xyzk S: portion of z = y2 over the square in the xy-plane with vertices (0, 0), (a, 0), (a, a), and (0, a)arrow_forward
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