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can be con cted by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: R₁ r(a) = r(b) R₁₂ Simply connected R3 ∞ Not simply connected Definition of a "simple" curve: A curve C given by r(t) = (x(t), y(t)), a≤t≤ b is simple if: That is: r(c) r(d) for any c and d in the open interval (a, b). C3-22-17.4 Green's Theorem Objectives: Use Green's Theorem to evaluate a line integral. ■Use alternative forms of Green's Theorem. page 1 of 8 We need to define a simply connected region before we can state Green's Theorem. Recall that a CONNECTED region means that any 2 points in the region can be connected by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: RA C r(a) = r(b) R₁₂ O R ∞

can be con cted by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: R₁ r(a) = r(b) R₁₂ Simply connected R3 ∞ Not simply connected Definition of a "simple" curve: A curve C given by r(t) = (x(t), y(t)), a≤t≤ b is simple if: That is: r(c) r(d) for any c and d in the open interval (a, b). C3-22-17.4 Green's Theorem Objectives: Use Green's Theorem to evaluate a line integral. ■Use alternative forms of Green's Theorem. page 1 of 8 We need to define a simply connected region before we can state Green's Theorem. Recall that a CONNECTED region means that any 2 points in the region can be connected by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: RA C r(a) = r(b) R₁₂ O R ∞

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Calculus lll 

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can be con cted by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: R₁ r(a) = r(b) R₁₂ Simply connected R3 ∞ Not simply connected Definition of a "simple" curve: A curve C given by r(t) = (x(t), y(t)), a≤t≤ b is simple if: That is: r(c) r(d) for any c and d in the open interval (a, b).
Transcribed Image Text:can be con cted by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: R₁ r(a) = r(b) R₁₂ Simply connected R3 ∞ Not simply connected Definition of a "simple" curve: A curve C given by r(t) = (x(t), y(t)), a≤t≤ b is simple if: That is: r(c) r(d) for any c and d in the open interval (a, b).
C3-22-17.4 Green's Theorem Objectives: Use Green's Theorem to evaluate a line integral. ■Use alternative forms of Green's Theorem. page 1 of 8 We need to define a simply connected region before we can state Green's Theorem. Recall that a CONNECTED region means that any 2 points in the region can be connected by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: RA C r(a) = r(b) R₁₂ O R ∞
Transcribed Image Text:C3-22-17.4 Green's Theorem Objectives: Use Green's Theorem to evaluate a line integral. ■Use alternative forms of Green's Theorem. page 1 of 8 We need to define a simply connected region before we can state Green's Theorem. Recall that a CONNECTED region means that any 2 points in the region can be connected by a lying entirely within the region. Here is a diagram of a simply connected region and a region that is not simply connected: RA C r(a) = r(b) R₁₂ O R ∞
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