Question

Consider the rotation field F = ?-y, x? and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral ?_C F · T ds is independent of the path, where C is a path from (1,0) to (0,1)? What is the value of the line integral for the path C1? (Type an exact answer, using ? as needed.)

          Consider the rotation field F = ?-y, x? and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral ?_C F · T ds is independent of the path, where C is a path from (1,0) to (0,1)?
What is the value of the line integral for the path C1?
(Type an exact answer, using ? as needed.)

Consider the rotation field F = ?-y, x? and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral ?C F · T ds is independent of the path, where C is a path from (1,0) to (0,1)?
What is the value of the line integral for the path C1?
(Type an exact answer, using ? as needed.)

Added by Jessica W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2022

Step 1

The line integral is given by: \[ \begin{aligned} \int_{C1} F \cdot dr & = \int_{0}^{1} (-1 + t)(1) dt \\ & = \int_{0}^{1} (-1 + t) dt \\ & = [-t + \frac{t^2}{2}]_{0}^{1} \\ & = -1 + \frac{1}{2} \\ & = -\frac{1}{2} \end{aligned} \] Show more…

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Consider the rotation field F = ⟨-y, x⟩ and the three paths shown in the figure. Compute the work done on each of the three paths. Does it appear that the line integral ∫_C F · T ds is independent of the path, where C is a path from (1,0) to (0,1)? What is the value of the line integral for the path C1? (Type an exact answer, using π as needed.)