Explanation For funding the line integral along the given path we have to parameterize the path and then convert to integral of single variable. Given: The path given in figure that described by x 2 + y 2 = 9 with x,y ≥ 0 and lines x = 0 , y = 0 Formula Used: ∫ c F . d r = ∫ c g ( t ) d t Calculation: By parameterizing the boundary of circle x = 3 cos t , y = 3 sin t with 0 ≤ t ≤ π 2 Now the line integral change as ∫ c y d x + x 2 y d y = ∫ 0 π / 2 3 sin t . d ( 3 c o s t ) + 9 cos 2 t .3 sin t . d ( 3 sin t ) = ∫ 0 π / 2 − 9 sin 2 t + 81 cos 3 t sin t d t = ∫ 0 π / 2 − 9 sin 2 t d t + ∫ 0 π / 2 81 cos 3 t sin t d t

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 17, Problem 34CRE

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To calculate: The line integral along given path.

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Chapter 17, Problem 33CRE

Chapter 17, Problem 35CRE

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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The line integral along given path.

Solution Summary: The author explains how to calculate the line integral along the given path by parameterizing the path and then converting it to integral of a single variable.

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Chapter 17 Solutions