Question

Find the circulation of F = 9xi + 9zj + 2yk around the closed path consisting of the following three curves traversed in the direction of increasing t. C?: r? (t) = (cos t)i + (sin t)j + tk, 0 ? t ??/2 C2: r2(t) = j + (?/2)(1-t)k, 0 ? t ?1 C3: r3(t)=ti+ (1-t)j, 0 ? t ? 1 The circulation is (Type an exact answer, using ? as needed.)

          Find the circulation of F = 9xi + 9zj + 2yk around the closed path consisting of the
following three curves traversed in the direction of increasing t.
C?: r? (t) = (cos t)i + (sin t)j + tk, 0 ? t ??/2
C2: r2(t) = j + (?/2)(1-t)k, 0 ? t ?1
C3: r3(t)=ti+ (1-t)j, 0 ? t ? 1
The circulation is 
(Type an exact answer, using ? as needed.)

Find the circulation of F = 9xi + 9zj + 2yk around the closed path consisting of the
following three curves traversed in the direction of increasing t.
C?: r? (t) = (cos t)i + (sin t)j + tk, 0 ? t ??/2
C2: r2(t) = j + (?/2)(1-t)k, 0 ? t ?1
C3: r3(t)=ti+ (1-t)j, 0 ? t ? 1
The circulation is
(Type an exact answer, using ? as needed.)

Added by Linda A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

12/06/2022

Step 1

Step 1: The circulation of a vector field F around a closed path C is given by the line integral ∫_C F · dr. Show more…

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Find the circulation of F = 9xi + 9zj + 2yk around the closed path consisting of the following three curves traversed in the direction of increasing t. C₁: r₁ (t) = (cos t)i + (sin t)j + tk, 0 ≤ t ≤π/2 C2: r2(t) = j + (π/2)(1-t)k, 0 ≤ t ≤1 C3: r3(t)=ti+ (1-t)j, 0 ≤ t ≤ 1 The circulation is (Type an exact answer, using π as needed.) (0, 1, C₁ C2 (1, 0, 0) (0,1,0) C3 y