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Exercise 18

Avg difficulty 2.5

Let C3C_3 be the circle of radius 77 centered at the origin traveled counterclockwise. Compute ∫C3⟨M,N⟩⋅dr⃗\int_{C_3} \langle M, N\rangle\cdot d\vr when:

  1. ⟨M,N⟩=⟨x,y⟩\langle M,N\rangle = \langle x,y \rangle

  2. ⟨M,N⟩=⟨−y,x⟩\langle M,N\rangle = \langle -y,x \rangle

  3. ⟨M,N⟩=⟨3,x⟩\langle M,N\rangle = \langle 3,x \rangle

Long, Keller & Schlicker, Active Calculus Multivariable, §13.4 Using Parameterizations to Calculate Line Integrals, Exercise 18

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.