Explanation Given: y = sin x , y = cos x Interval: [ 0, π 4 ] Formula Used: x ¯ = ∫ a b x [ f ( x ) − g ( x ) ] d x ∫ a b [ f ( x ) − g ( x ) ] d x and y ¯ = ∫ a b 1 2 [ f ( x ) 2 − g ( x ) 2 ] d x ∫ a b [ f ( x ) − g ( x ) ] d x Let, y = g ( x ) = sin x , y = f ( x ) = cos x . It is given that a = 0 , b = π 4 . Now substituting these in the formulae for x ¯ and y ¯ , we get x ¯ = ∫ a b x [ f ( x ) − g ( x ) ] d x ∫ a b [ f ( x ) − g ( x ) ] d x ∫ a b [ f ( x ) − g ( x ) ] d x = ∫ 0 π 4 [ cos ( x ) − sin ( x ) ] d x = [ sin ( x ) + cos ( x ) ] 0 π 4 = [ sin ( π 4 ) + cos ( π 4 ) − sin ( 0 ) − cos ( 0 ) ] = [ 1 2 + 1 2 − 0 − 1 ] = 2 2 − 1 = 2 − 1 Now, to integrate the numerator, we use integration by parts u = x , d v = [ cos ( x ) − sin ( x ) ] d x ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.4, Problem 29E

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To findthe centroid of the region lying between the graphs of the functions, in the interval of $[0, \frac{π}{4}]$ .

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Chapter 9.4, Problem 28E

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To findthe centroid of the region lying between the graphs of the functions, in the interval of [ 0, π 4 ] .

Solution Summary: The author explains how to determine the centroid of the region lying between the graphs of functions, in the interval of [ 0, 4 ].

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To findthe centroid of the region lying between the graphs of the functions, in the interval of $[0, \frac{π}{4}]$ .

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Chapter 9 Solutions

To findthe centroid of the region lying between the graphs of the functions, in the interval of [ 0, π 4 ] .

Solution Summary: The author explains how to determine the centroid of the region lying between the graphs of functions, in the interval of [ 0, 4 ].

Videos

To findthe centroid of the region lying between the graphs of the functions, in the interval of [0,π4].

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Chapter 9 Solutions

To findthe centroid of the region lying between the graphs of the functions, in the interval of $[0, \frac{π}{4}]$ .