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93. Prove that the area of a circle of radius r is r², as follows: (a) Write down a definite integral that represents the area of the circle of radius r centered at the origin. (Hint: The equation of such a circle is x? + y? = r².) (b) Use trigonometric substitution to solve the definite integral you found in part (a). (Hint: Change the limits of integration to match your substitution.)

93. Prove that the area of a circle of radius r is r², as follows: (a) Write down a definite integral that represents the area of the circle of radius r centered at the origin. (Hint: The equation of such a circle is x? + y? = r².) (b) Use trigonometric substitution to solve the definite integral you found in part (a). (Hint: Change the limits of integration to match your substitution.)

Calculus: Early Transcendentals
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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93. Prove that the area of a circle of radius r is r², as follows: (a) Write down a definite integral that represents the area of the circle of radius r centered at the origin. (Hint: The equation of such a circle is x? + y? = r².) (b) Use trigonometric substitution to solve the definite integral you found in part (a). (Hint: Change the limits of integration to match your substitution.)
Transcribed Image Text:93. Prove that the area of a circle of radius r is r², as follows: (a) Write down a definite integral that represents the area of the circle of radius r centered at the origin. (Hint: The equation of such a circle is x? + y? = r².) (b) Use trigonometric substitution to solve the definite integral you found in part (a). (Hint: Change the limits of integration to match your substitution.)
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