Consider the vector field F = (2xy³ − y sin x)i + (3x²y² + cos x)j (a) Determine whether F is conservative. If conservative, find a scalar potential. (b) Compute F. dr where C is parameterized by r = (t², t³) for 0 ≤ t ≤ 1.

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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Consider the vector field F = (2xy³ − y sin x)i + (3x²y² + cos x)j
(a) Determine whether F is conservative. If conservative, find a scalar potential.
(b) Compute F. dr where C is parameterized by r = (t², t³) for 0 ≤ t ≤ 1.
Transcribed Image Text:Consider the vector field F = (2xy³ − y sin x)i + (3x²y² + cos x)j (a) Determine whether F is conservative. If conservative, find a scalar potential. (b) Compute F. dr where C is parameterized by r = (t², t³) for 0 ≤ t ≤ 1.
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