Explanation Given information: ∫ 0 2 4 − x 4 ⋅ 2 x d x , and the area of the circle of radius r is π r 2 . Formula Used: 1 ) Change of limits rule: ∫ a b f ( g ( x ) ) g ' ( x ) d x = ∫ g ( a ) g ( b ) f ( u ) d u , If g ( x ) = u and g ' ( x ) d x = d u 2 ) Function of a circle of radius r and center at point ( 0 , 0 ) is y = r 2 − x 2 Calculation: Here f ( g ( x ) ) = 4 − x 4 = 2 2 − ( x 2 ) 2 and a = 0 , b = 2 Therefore, g ( x ) = x 2 At a = 0 ⇒ g ( a ) = g ( 0 ) = ( 0 ) 2 = 0 and At b = 2 ⇒ g ( b ) = g ( 2 ) = ( 2 ) 2 = 2 Consider, g ( x ) = u = x 2 Differentiate with respect to x d u d<

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Author: Larry Goldstein / David Lay

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Chapter 9.3, Problem 22E

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To calculate: ∫02 4 − x4 ⋅ 2x dx.

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Chapter 9.3, Problem 21E

Chapter 9.3, Problem 23E

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∫ 0 2 4 − x 4 ⋅ 2 x d x .

Solution Summary: The author explains how to calculate the value of a circle of radius r and the area of the circle.

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Chapter 9 Solutions