Explanation In simple words, arc length is defined as the length of a curve or line. The length of an arc can be found by one of the formulas below for any differentiable curve (function) defined by rectangular, polar, or parametric equations. Mathematically, the integral of a function over an interval [ a , b ] is known as the arc length of the curve or function. It defines the area under the function over that interval. This process of determining the arc length of a curve (function) is called rectifying the curve. For any real-valued function y = f ( x ) and d y d x = f ' ( x ) are continuous over the interval [ a , b ] the arc length s of the curve is defined as s = ∫ a b d s . Depending on the form of the function, ds has different forms: i) for rectangular coordinates, d s = 1 + ( d y d x ) 2 d x ii) for polar coordinates, d s = r 2 + ( d r d θ ) 2 d θ iii) for parametric equations, d s = ( d x d t ) 2 + ( d y d t ) 2 d t Given: To define arc length. Formula used: For any real-valued function y = f ( x ) and d y d x = f ' ( x ) are continuous over the interval [ a , b ] the arc length s of the curve is defined as s = ∫ a b d s . Depending on the form of the function, ds has different forms: i) for rectangular coordinates, d s = 1 + ( d y d x ) 2 d x ii) for polar coordinates, d s = r 2 + ( d r d θ ) 2 d θ iii) for parametric equations, d s = ( d x d t ) 2 + ( d y d t ) 2 d t Calculation: In simple words, arc length is defined as the length of a curve or line. The length of an arc can be found by one of the formulas below for any differentiable curve (function) defined by rectangular, polar, or parametric equations. Mathematically, the integral of a function over an interval [ a , b ] is known as the arc length of the curve or function...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.2, Problem 1PQ

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What is arc length?

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Chapter 12.1, Problem 109E

Chapter 12.2, Problem 2PQ

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Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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What is arc length?

Solution Summary: The author explains that arc length is defined as the length of a curve or line. It can be found by formulas for any differentiable curve defined by rectangular, polar, or parametric equations.

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Chapter 12 Solutions

To Explain:

What is arc length?