To illustrate thefact that the numbers we get for length do not depend on the waywe parametrize our curves (except for the mild restrictions preventingdoubling back mentioned earlier), calculate the length ofthe semicircle y = √(1 - x2) with these two different parametrizations: x = sin πt, y = cos πt, -1/2 ≤ t ≤ 1/2.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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To illustrate the
fact that the numbers we get for length do not depend on the way
we parametrize our curves (except for the mild restrictions preventing
doubling back mentioned earlier), calculate the length of
the semicircle y = √(1 - x2) with these two different parametrizations: x = sin πt, y = cos πt, -1/2 ≤ t ≤ 1/2.

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