Explanation Given: The functions are f ( x ) = sin x , g ( x ) = sin 2 x , π 3 ≤ x ≤ π . Formula used: Area of the region A = ∫ a b [ ( Upper function ) − ( Lower function ) ] d x Where a ≤ x ≤ b . Calculation: The functions are f ( x ) = sin x , g ( x ) = sin 2 x , π 3 ≤ x ≤ π . We can rewrite it as: y = sin x , y = sin 2 x The graphs of y = sin x and y = sin 2 x intersect where sin x = sin 2 x sin x = 2 sin x cos x sin x sin x cos x = 2 sec x = 2 We know that, sec π 3 = 2 . sec x = sec π 3 x = π 3 The graph of the function is: Thus, the enclosed area lies over the interval [ π 3 , π ] . The region enclosed by the graphs of y = sin x , y = sin 2 x over the interval [ π 3 , π ] ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6, Problem 10CRE

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

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

Solution Summary: The function is f (x) = sin x, g (y )= sin 2. The graphs of y, sin, and sin are intersected over the interval.

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Chapter 6 Solutions