Explanation Given: c ( t ) = ( e − t cos t , e − t sin t ) for 0 ≤ t < ∞ . Formula Used: The length of a curve c ( t ) from t = a to t = b will be given by: L = ∫ t = a t = b ( d x d t ) 2 + ( d y d t ) 2 d t Calculation: It is given that c ( t ) = ( e − t cos t , e − t sin t ) that means we have x ( t ) = e − t cos t , y ( t ) = e − t sin t . Now, differentiate both the equations x ( t ) = e − t cos t , y ( t ) = e − t sin t with respect to t and we get: x ( t ) = e − t cos t , y ( t ) = e − t sin t d x d t = − e − t ( cos t + sin t ) , d y d t = e − t ( cos t − sin t ) So, ( d x d t ) 2 + ( d y d t ) 2 = ( − e − t ( cos t + sin t ) ) 2 + ( e − t ( cos t −

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 12, Problem 23CRE

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That $c (t)$ for $0 \leq t < \infty$ has finite length and to determine its length

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Chapter 12, Problem 22CRE

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That c ( t ) for 0 ≤ t < ∞ has finite length and to determine its length

That $c (t)$ for $0 \leq t < \infty$ has finite length and to determine its length