Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment from (0, 0) to (-1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (-1,-1) traced counterclockwise.
Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment from (0, 0) to (-1, 1), and C3 is the portion of the circle x² + y² = 2 from (-1, 1) to (-1,-1) traced counterclockwise.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 44E
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Answer a AND B
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![Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line
segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to
(-1,-1) traced counterclockwise.
Define F(x, y) =<;
+tan ¹y,
+ 3y² >.
1+y²
a. Show that is conservative by finding all its potential functions.
b. Based on (a), what is the value of Sc F.dR?
2 √x+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1de94a93-f086-40f0-9aea-f285b8c16e93%2Ff9bc2023-bb75-44c2-87c4-e8ce5c379926%2Ftltvrha_processed.png&w=3840&q=75)
Transcribed Image Text:Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line
segment from (0, 0) to (−1, 1), and C3 is the portion of the circle x² + y² = 2 from (−1, 1) to
(-1,-1) traced counterclockwise.
Define F(x, y) =<;
+tan ¹y,
+ 3y² >.
1+y²
a. Show that is conservative by finding all its potential functions.
b. Based on (a), what is the value of Sc F.dR?
2 √x+2
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