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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

Consider the vector field F = (-4,5). Let C be the straight line segment oriented from point
(4,0) to point (0, 3); C has parameterization F(t) = (4(1-t), 3t) for 0 ≤ t ≤ 1.
Compute the flux of F across C.
Flux =
Evaluate F. dr, where F = (5yz, 5x2 + 4, 5xy + 2z) and C is defined by
x=t², y=t+5, z = 4t-5, 0 < t < 4. Note that F= Vf where
f(x, y, z) = 5xyz + 4y + 2².
[F. dr, where F(x, y) = < 32², 3y²> and C is the line segment from (0, 0) to
Evaluate
(3, 1) followed by the segment from (3, 1) to (4,3).
Vf where f(x, y) = x³ + y³.
Note that F
=

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