Explanation Given: The provided function is y = arcsin x , y = 0 and x = π 2 . Formula used: Area of the region: A = ∫ a b f ( x ) d x Equation of moments: M x = ρ ∫ a b 1 2 [ ( f ( x ) ) 2 − ( g ( x ) ) 2 ] d x M y = ρ ∫ a b x [ f ( x ) − g ( x ) ] d x Whereas, ρ is the density. Centroid: x ¯ = M y M , y ¯ = M x M Whereas, M is mass of the bounded region. M = ρ ⋅ A Calculation: Consider the function y = arcsin x , Tabular form of a function is: x − 1 0 1 y = arcsin x − π 2 0 π 2 There the area bounded by the graph is: Now, area of graph between x = − 1 , and x = 1 is, A = ∫ 0 1 ( π 2 − arcsin x ) d x = [ π 2 x − x arcsin x − 1 − x 2 ] 0 1 = [ π 2 − π 2 − 0 ] − [ − 1 ] = 1 Now use equation of moments to get center of mass, M x = ρ ∫ a b 1 2 [ ( f ( x ) ) 2 − ( g ( x ) ) 2 ] d x M y = ρ ∫ a b x [ f ( x ) − g ( x ) ] d x For x ¯ , x ¯ = M y M = ρ ∫ a b x [ f ( x ) − g ( x ) ] d x ρ ⋅ A = ∫ 0 1 x ( π 2 − arcsin x ) d x 1 = [ 1 4 x 2 ( <

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ISBN: 9781337678445

Author: Larson, Edward

Publisher: CENGAGE L

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Chapter 8.2, Problem 89E

To determine

To calculate: The centroid of the region bounded by the graph of y=arcsinx, y=0 and x=π2.

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Chapter 8.2, Problem 88E

Chapter 8.2, Problem 90E

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Chapter 8 Solutions

CALCULUS EARLY TRANSCENDENTAL FUNCTIONS

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The centroid of the region bounded by the graph of y = arcsin x , y = 0 and x = π 2 .

To calculate: The centroid of the region bounded by the graph of y=arcsinx, y=0 and x=π2.

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Chapter 8 Solutions