Explanation 1) Concept: Formula: The area A of the region bounded by the curves y = f ( x ) , y = g ( x ) and the lines x = a a n d x = b is A = ∫ a b f x - g x d x f x - g x = f x - g x w h e n f x ≥ g ( x ) g x - f x w h e n g x ≥ f ( x ) 2) Given: y = cos 2 ⁡ x sin ⁡ x , y = sin ⁡ x , 0 ≤ x ≤ π 3) Calculation: First, find the intersection points of the curves by solving their equations simultaneously. cos 2 ⁡ x sin ⁡ x = sin ⁡ x This gives, cos 2 ⁡ x sin ⁡ x - sin ⁡ x = 0 sin ⁡ x c o s 2 x - 1 = 0 sin ⁡ x sin 2 ⁡ x = 0 Therefore, sin ⁡ x = 0 Which gives the boundary points of the region as x = 0 and π

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.1, Problem 31E

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The sketch the region enclosed by the given curves and find its area

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Chapter 5.1, Problem 30E

Chapter 5.1, Problem 32E

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To: The sketch the region enclosed by the given curves and find its area

Solution Summary: The author explains how to find the intersection points of the curves by solving their equations simultaneously.