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(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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