Evaluating line integrals Evaluate the line integral ∫C F ⋅ drfor the following vector fields F and curves C in two ways.a. By parameterizing Cb. By using the Fundamental Theorem for line integrals, if possible F = ∇(x2y); C: r(t) = ⟨9 - t2, t⟩ , for 0 ≤ t ≤ 3

Evaluating line integrals Evaluate the line integral ∫C F ⋅ drfor the following vector fields F and curves C in two ways.a. By parameterizing Cb. By using the Fundamental Theorem for line integrals, if possible F = ∇(x2y); C: r(t) = ⟨9 - t2, t⟩ , for 0 ≤ t ≤ 3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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Question

Evaluating line integrals Evaluate the line integral ∫_C F ⋅ dr
for the following vector fields F and curves C in two ways.
a. By parameterizing C
b. By using the Fundamental Theorem for line integrals, if possible

F = ∇(x²y); C: r(t) = ⟨9 - t², t⟩ , for 0 ≤ t ≤ 3

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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