Find the circulation of F = 2x i + 6z j + 3y k 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 + t k, 0 ? t ? ?/2 C2 r2(t) = i + (?/2)(1 - t) j + t k, 0 ? t ? 1 C3 r3(t) = t i + (1 - t) j, 0 ? t ? 1 The circulation is (Type an exact answer, using ? as needed): (3/4)?^2 - (3/4)? + 3
Added by Michael G.
Close
Step 1
** Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 55 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the circulation of F = 8xi + 9zj + 6yk 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
Madhur L.
Find the circulation of F = 3xi + 6zj + 3yk 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 ≤ ̴̵̶̷̸̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎̀́̂̃̄̅̆̇̈̉̊̋̌̍̎̏̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡ͰͱͲͳʹ͵Ͷͷͺͻͼͽ;Ϳ΄΅Ά·ΈΉΊΌΎΏΐπ/2 c2: r2(t) = j + (π/2)(1 - t)k, 0 ≤ t ≤ 1 c3: r3(t) = ti + (1 - t)j, 0 ≤ t ≤ 1.
Consider the following vector fields $\mathbf{F}$ and closed oriented curves $C$ in the plane (see figures). a. Based on the picture, make a conjecture about whether the circulation of on C is positive, negative, or zero. b. Compute the circulation and interpret the result. $$\mathbf{F}=\frac{\langle y,-2 x\rangle}{\sqrt{4 x^{2}+y^{2}}} ; C: \mathbf{r}(t)=\langle 2 \cos t, 4 \sin t\rangle, \text { for } 0 \leq t \leq 2 \pi$$ (FIGURE CAN'T COPY).
Vector Calculus
Line Integrals
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD