(a) the quarter-circle C₁ from P(1,0) to Q(0, 1): r(t) = (cost, sin t), 0 ≤ t ≤ (b) the quarter-circle -C₁ from Q(0, 1) to P(1,0): r(t) = (sint, cost), 0 ≤ t ≤ (c) the path C₂ from Q(0, 1) to P(1,0) consisting of two line segments through the origin: ri(t) = (0, 1 – t), 0 ≤ t ≤ 1 followed by r₂(t) = (t, 0), 0 ≤ t ≤ 1.
(a) the quarter-circle C₁ from P(1,0) to Q(0, 1): r(t) = (cost, sin t), 0 ≤ t ≤ (b) the quarter-circle -C₁ from Q(0, 1) to P(1,0): r(t) = (sint, cost), 0 ≤ t ≤ (c) the path C₂ from Q(0, 1) to P(1,0) consisting of two line segments through the origin: ri(t) = (0, 1 – t), 0 ≤ t ≤ 1 followed by r₂(t) = (t, 0), 0 ≤ t ≤ 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![1. Evaluate the integral [F.Tds with F = (-2,y) on the following oriented paths in R²:
π
(a) the quarter-circle C₁ from P(1, 0) to Q(0, 1): r(t) = (cost, sin t), 0 ≤ t ≤
(b) the quarter-circle -C₁ from Q(0, 1) to P(1,0): r(t) = (sint, cost), 0 ≤ t ≤
(c) the path C₂ from Q(0, 1) to P(1,0) consisting of two line segments through the origin:
ri(t) = (0, 1 t), 0≤ t ≤ 1 followed by F2(t) = (t,0), 0≤ t ≤ 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2755b6-7089-4f85-a844-ede57d3c63f1%2Fe97bfd94-3d53-42cf-8e10-cb0aea9821b5%2Fbu9gm56j.jpeg&w=3840&q=75)
Transcribed Image Text:1. Evaluate the integral [F.Tds with F = (-2,y) on the following oriented paths in R²:
π
(a) the quarter-circle C₁ from P(1, 0) to Q(0, 1): r(t) = (cost, sin t), 0 ≤ t ≤
(b) the quarter-circle -C₁ from Q(0, 1) to P(1,0): r(t) = (sint, cost), 0 ≤ t ≤
(c) the path C₂ from Q(0, 1) to P(1,0) consisting of two line segments through the origin:
ri(t) = (0, 1 t), 0≤ t ≤ 1 followed by F2(t) = (t,0), 0≤ t ≤ 1.
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