In Exercises 1-5 find ſc M(x, y) dx + N(x, y) dy, where C is oriented counterclockwise. 1. M(x, y) = y, N(x, y) = 0; C is composed of the portion of the quarter circle x² + 1² = 4 in the first quadrant and of the intervals [0, 2] on the x and y axes. 2. M(x, y) = 0, N(x, y) = x; C is the circle x² + 1 2² = 9. 3. M(x, y) = xy, N(x, y) = x³/2 + y³/2; C is the square with vertices (0, 0), (1, 0), (1, 1), and (0, 1). 4. M(x, y) = y cos x, N(x, y) = x sin y; C is the triangle with vertices (0, 0), (π/2, 0), and (0, π/2).
In Exercises 1-5 find ſc M(x, y) dx + N(x, y) dy, where C is oriented counterclockwise. 1. M(x, y) = y, N(x, y) = 0; C is composed of the portion of the quarter circle x² + 1² = 4 in the first quadrant and of the intervals [0, 2] on the x and y axes. 2. M(x, y) = 0, N(x, y) = x; C is the circle x² + 1 2² = 9. 3. M(x, y) = xy, N(x, y) = x³/2 + y³/2; C is the square with vertices (0, 0), (1, 0), (1, 1), and (0, 1). 4. M(x, y) = y cos x, N(x, y) = x sin y; C is the triangle with vertices (0, 0), (π/2, 0), and (0, π/2).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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