Explanation Given: The functions are y = sin x , y = cos x , 0 ≤ x ≤ 5 π 4 . Formula used: Area of the region A = ∫ a b [ ( Upper function ) − ( Lower function ) ] d x Where a ≤ x ≤ b . Calculation: The functions are y = sin x , y = cos x , 0 ≤ x ≤ 5 π 4 . The graphs of y = sin x , y = cos x intersect where sin x = cos x sin x cos x = 1 tan x = 1 We know that, tan π 4 = 1 . tan x = tan π 4 x = π 4 The graph of the function is: Thus, the enclosed area lies over the interval [ 0 , 5 π 4 ] . The region enclosed by the graphs of y = sin x , y = cos x over the interval [ 0 , 5 π 4 ] . The graph of y = cos x lies above the graph of y = sin x for the interval [ 0 , π 4 ] and the graph of y = sin x lies above the graph of y = cos x for the interval [ π 4 , 5 π 4 ] . Now, find the area. Area = ∫ 0 π 4 [ cos x − sin x ] d x + ∫ π 4 5 π 4 [ sin x − cos x ] d x Solve the integral...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6, Problem 9CRE

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Compute the area of the region enclosed by the graphs of the function.

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Chapter 6, Problem 8CRE

Chapter 6, Problem 10CRE

Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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Compute the area of the region enclosed by the graphs of the function.

Solution Summary: The graphs of y = sin x & cos X intersect where tan 4 = 1. The area of the enclosed region is 3 21

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Compute the area of the region enclosed by the graphs of the function.

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Chapter 6 Solutions