Explanation Formula used: ∫ C F ⋅ d r = ∫ C F ( r ( t ) ) ⋅ r ′ ( t ) d t Calculations: Given F ( x , y ) = 〈 2 x y , x 2 + y 2 〉 Andthe given path is the part of the unit circle in the first quadrant oriented counterclockwise. The parametric form of such a curve is r ( t ) = 〈 cos t , sin t 〉 for 0 ≤ t ≤ π 2 Since r ( t ) = 〈 cos t , sin t 〉 , so x = cos t , y = sin t Thus, F ( x , y ) = 〈 2 x y , x 2 + y 2 〉 F ( r ( t ) ) = 〈 2 cos t sin t , cos 2 t + sin 2 t 〉 = 〈 2 cos t sin t , 1 〉 Now, since r ( t ) = 〈 cos t , sin t 〉 , so d r = r ′ ( t ) d t d r = 〈 − sin t , cos t 〉 d t Thus, F ( r (

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17, Problem 37CRE

To determine

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

$F (x, y) = 〈 2 x y, x^{2} + y^{2} 〉$ , the part of the unit circle in the first quadrant oriented counterclockwise.

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Chapter 17, Problem 36CRE

Chapter 17, Problem 38CRE

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Chapter 17 Solutions

CALCULUS (CLOTH)

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

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To compute the line integral ∫ C F ⋅ d r : For the given vector field F ( x , y ) = 〈 2 x y , x 2 + y 2 〉 , the part of the unit circle in the first quadrant oriented counterclockwise.

Solution Summary: The author explains how to compute the line integral C F, d r, and the parametric form of the curve.

Concept explainers

Videos

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

$F (x, y) = 〈 2 x y, x^{2} + y^{2} 〉$ , the part of the unit circle in the first quadrant oriented counterclockwise.

Want to see the full answer?

Chapter 17 Solutions

To compute the line integral ∫ C F ⋅ d r : For the given vector field F ( x , y ) = 〈 2 x y , x 2 + y 2 〉 , the part of the unit circle in the first quadrant oriented counterclockwise.

Solution Summary: The author explains how to compute the line integral C F, d r, and the parametric form of the curve.

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To compute the line integral∫CF⋅dr: For the given vector field F(x,y)=〈2xy,x2+y2〉, the part of the unit circle in the first quadrant oriented counterclockwise.

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Chapter 17 Solutions

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

$F (x, y) = 〈 2 x y, x^{2} + y^{2} 〉$ , the part of the unit circle in the first quadrant oriented counterclockwise.