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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Doing textbook problems for quiz prep. Can you show me how to solve number 4? Show each step please, even the oness you feel are obvious.
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fb406b3-dfb5-4d65-a424-9ec71ae4c6de%2F0cc9f356-49f7-4af8-b505-94b45bf7f745%2Fkfbhuqt_processed.png&w=3840&q=75)
Transcribed Image Text: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).
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