2. (a) Show that F(x, y) = x³yt i + x+y³ j is a conservative vector field. (b) For the vector field F(x, y) = x³y4 i+ x4y3 j find a function f such that Vf = F. (c) Evaluate the line integral F dr where C is the curve given by r(t) = (t3 – 2t, t3 + 2t), 0 st s 1. (d) Which method did you use to calculate fF dr in question (c)? Would the method be still valid if F would not be a conservative vector field?

2. (a) Show that F(x, y) = x³yt i + x+y³ j is a conservative vector field. (b) For the vector field F(x, y) = x³y4 i+ x4y3 j find a function f such that Vf = F. (c) Evaluate the line integral F dr where C is the curve given by r(t) = (t3 – 2t, t3 + 2t), 0 st s 1. (d) Which method did you use to calculate fF dr in question (c)? Would the method be still valid if F would not be a conservative vector field?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 16P

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