Show the vector field V = (8xy³ z, 12x²y² z, 4x²y³) is irrotational, and find its potential. Then, by using the Path Independence Integral, and the Fundamental Theorem of Calculus for Vector Fields evaluate the line integral along the helix parameterized by F(t)= (2 cos t, 2 sin t, t) from (2, 0, 0) to (1, √3, π/3)

Show the vector field V = (8xy³ z, 12x²y² z, 4x²y³) is irrotational, and find its potential. Then, by using the Path Independence Integral, and the Fundamental Theorem of Calculus for Vector Fields evaluate the line integral along the helix parameterized by F(t)= (2 cos t, 2 sin t, t) from (2, 0, 0) to (1, √3, π/3)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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