Explanation Given: Let F be the vortex field (so-called because it swirls around the origin): F ( x , y ) = 〈 − y x 2 + y 2 , x x 2 + y 2 〉 . Let a > 0 , b < c . Proof: Parameterized the line segment joining P = ( a , b ) and Q = ( a , c ) and we get: c ( t ) = ( a , t ) , b ≤ t ≤ c Now, calculate the vortex field along the line segment and we get: F ( c ( t ) ) = 〈 − t a 2 + t 2 , a a 2 + t 2 〉 Now, the line integral is: ∫ C F d s = ∫ b c F ( c ( t ) ) c ' (

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.2, Problem 62E

To determine

To prove:

The integral of $F$ along the segment from $P = (a, b)$ to $Q = (a, c)$ is equal to the angle $∠ P O Q$ .

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Chapter 17.2, Problem 61E

Chapter 17.2, Problem 63E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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To prove: The integral of F along the segment from P = ( a , b ) to Q = ( a , c ) is equal to the angle ∠ P O Q .

Solution Summary: The author proves that the integral of F along the segment from P = (a, b ) to Q =

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To prove:

The integral of $F$ along the segment from $P = (a, b)$ to $Q = (a, c)$ is equal to the angle $∠ P O Q$ .

Want to see the full answer?

Chapter 17 Solutions

To prove: The integral of F along the segment from P = ( a , b ) to Q = ( a , c ) is equal to the angle ∠ P O Q .

Solution Summary: The author proves that the integral of F along the segment from P = (a, b ) to Q =

Concept explainers

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To prove: The integral of F along the segment from P=(a,b) to Q=(a,c) is equal to the angle ∠POQ.

Want to see the full answer?

Chapter 17 Solutions

To prove:

The integral of $F$ along the segment from $P = (a, b)$ to $Q = (a, c)$ is equal to the angle $∠ P O Q$ .