Question

Let \(F = \left(2xy - z^2, x^2 + yz, -2xz + \frac{y^2}{2}\right)\) and let C be the circle \(r(t) = (2\cos t, 5\sin t, 6\sin t)\), for \(0 \le t \le 2\pi\). Evaluate \(\oint_C F \cdot dr\) using any method. \(\oint_C F \cdot dr = \boxed{}\) (Simplify your answer.)

          Let \(F = \left(2xy - z^2, x^2 + yz, -2xz + \frac{y^2}{2}\right)\) and let C be the circle \(r(t) = (2\cos t, 5\sin t, 6\sin t)\), for \(0 \le t \le 2\pi\). Evaluate \(\oint_C F \cdot dr\) using any method.
\(\oint_C F \cdot dr = \boxed{}\) (Simplify your answer.)

Let F = (2xy - z^2, x^2 + yz, -2xz + (y^2)/(2)) and let C be the circle r(t) = (2cos t, 5sin t, 6sin t), for 0 ≤ t ≤ 2π. Evaluate F · dr using any method.
F · dr = (Simplify your answer.)

Added by Shawn W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

04/25/2022

Step 1

Step 1: First, we need to parameterize the curve C using the given equation r(t)=2 cos t,5 sin t,6 sin t). Show more…

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. Let F= [2xy -z2,x2+ yz, -2xz + and let C be the circle r(t)=2 cos t,5 sin t,6 sin t), for 0t2. Evaluate F dr using any method. c F dr=(Simplify your answer.)