Explanation Given: Thefunction 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 Where ρ is the density. Centroid coordinates are given by: x ¯ = M y M , y ¯ = M x M where, M denote themass of the bounded region. M = ρ ⋅ A Calculation: Consider the following function, y = arcsin x , Now, make a table form theabove function as follows: x − 1 0 1 y = arcsin x − π 2 0 π 2 The area bounded by the graph as shown below, Now, calculate the area of graph between x = − 1 , and x = 1 as, 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, we will use the 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 = [

Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term

10th Edition

ISBN: 9781305718661

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Question

Chapter 8.2, Problem 85E

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 84E

Chapter 8.2, Problem 86E

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Chapter 8 Solutions

Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 6E Ch. 8.1 - Choosing a Formula In Exercises 514, select the...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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

Solution Summary: The author explains how to calculate the centroid of the region bounded by the graph of y=mathrmarcsinx.

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