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...

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ISBN: 9781319323394

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.

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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