To compute the line integral ∫ C F ⋅ d r : For the given vector field F ( x , y ) = 〈 2 y x 2 + 4 y 2 , x x 2 + 4 y 2 〉 , the path r ( t ) = 〈 cos t , 1 2 sin t 〉 for 0 ≤ t ≤ 2 π

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Answer 1

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Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

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Answer 2

Question

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

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Answer 3

Question

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

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Answer 4

Question

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

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Answer 5

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

Answer 6

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

Answer 7

Chapter 17, Problem 36CRE

To determine

To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

To compute the line integral ∫ C F ⋅ d r : For the given vector field F ( x , y ) = 〈 2 y x 2 + 4 y 2 , x x 2 + 4 y 2 〉 , the path r ( t ) = 〈 cos t , 1 2 sin t 〉 for 0 ≤ t ≤ 2 π

Solution Summary: The author explains the formula used to compute the line integral, C F d r, for the given vector field.

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To compute the line integral $\int_{C} F \cdot d r$ : For the given vector field

$F (x, y) = 〈 \frac{2 y}{x^{2} + 4 y^{2}}, \frac{x}{x^{2} + 4 y^{2}} 〉$ , the path $r (t) = 〈 \cos t, \frac{1}{2} \sin t 〉 for 0 \leq t \leq 2 π$

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Chapter 17 Solutions

To compute the line integral ∫ C F ⋅ d r : For the given vector field F ( x , y ) = 〈 2 y x 2 + 4 y 2 , x x 2 + 4 y 2 〉 , the path r ( t ) = 〈 cos t , 1 2 sin t 〉 for 0 ≤ t ≤ 2 π

Solution Summary: The author explains the formula used to compute the line integral, C F d r, for the given vector field.

Concept explainers

Videos