1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √1-x². (a) Explain why y = √1- x² gives only the top half of the circle. (d) Try instead the substitution x = = sin(). (Hint: The identity sin² (0) + cos² (0) = 1 will be helpful.) Does this substitution work better? You do not need to complete the integral.
1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √1-x². (a) Explain why y = √1- x² gives only the top half of the circle. (d) Try instead the substitution x = = sin(). (Hint: The identity sin² (0) + cos² (0) = 1 will be helpful.) Does this substitution work better? You do not need to complete the integral.
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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Transcribed Image Text:1. The equation x² + y² = 1 describes a circle of radius 1. Solving for y, we get y = √1 – x².
(a) Explain why y
√1 - x² gives only the top half of the circle.
=
(d) Try instead the substitution x = = sin(0). (Hint: The identity sin²(0) + cos² (0) = 1 will be
helpful.) Does this substitution work better? You do not need to complete the integral.
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