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Exercise 17

Avg difficulty 2.5

If the wind in a region of space is given by F⃗=⟨y+z,z−x,−z⟩\vF=\langle y+z,z-x,-z \rangle and a helicopter flies along the path given by r⃗(t)=⟨10sin⁡(t),10cos⁡(t),(10−t)2⟩\vr(t) = \langle 10 \sin(t),10\cos(t),(10-t)^2 \rangle as 0≤t≤4π0\leq t\leq4\pi. Calculate the work done by the wind on the helicopter.

Long, Keller & Schlicker, Active Calculus Multivariable, §13.4 Using Parameterizations to Calculate Line Integrals, Exercise 17

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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.