Explanation Given: y = sin − 1 x f o r 0 ≤ x ≤ 1 Calculation: Consider a line y = k bisects the area under the curve y = sin − 1 x f o r 0 ≤ x ≤ 1 Consider the region is bounded by the curve inside the interval [ 0 , π 2 ] x = sin y x = 1 Consider the area bounded by the curve x = f ( y ) , x = g ( y ) inside the interval [a, b] with f ( y ) ≥ g ( y ) is A = ∫ a b { f ( y ) − g ( y ) } d y Consider the area inside the interval y ∈ [ 0 , k ] A i = ∫ 0 k ( 1 − sin y ) d y = ( y + cos y ) | 0 π 2 = k + cos k − 0 −

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.1, Problem 45PS

To determine

To find: the number k so that the line y=k bisects the area under the curve

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Chapter 6.1, Problem 44PS

Chapter 6.1, Problem 46PS

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Chapter 6 Solutions

Calculus

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the number k so that the line y = k bisects the area under the curve

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Chapter 6 Solutions