Explanation Given: The derivative of the function is: f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 ; ( 2 , 10 ) Formula used: If f ' ( x ) is derivative of f ( x ) . Then, ∫ f ' ( x ) d x = f ( x ) The integration of x n is: ∫ x n d x = x n + 1 n + 1 + C The change of variable theorem for the indefinite integral: If u = g ( x ) . Then d u = g ' ( x ) d x . Then, the integral will take the following form: ∫ f ( g ( x ) ) g ' ( x ) d x = ∫ f ( u ) d u = F ( u ) + C Calculation: Consider the provided derivative of the function, f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 To find the equation of the function f ( x ) , integrate f ' ( x ) with respect to x . Then, f ( x ) = ∫ f ' ( x ) d x = ∫ 2 x ( 4 x 2 − 10 ) 2 d x Let, ( 4 x 2 − 10 ) = u

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Chapter 4.5, Problem 51E

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To calculate: The equation of the function whose derivative is given f'(x)=2x(4x2−10)2 ;(2,10).

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Chapter 4.5, Problem 48E

Chapter 4.5, Problem 52E

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The equation of the function whose derivative is given f ' ( x ) = 2 x ( 4 x 2 − 10 ) 2 ; ( 2 , 10 ) .

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To calculate: The equation of the function whose derivative is given f'(x)=2x(4x2−10)2 ;(2,10).

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