Explanation Obtain the anti-derivative of the given function f ( x ) = 3 2 ( 6 x + 1 ) 1 2 ( 6 ) as follows. Form the anti-derivative by increasing the power of x in f ( x ) by 1. F ( x ) = a ( 6 x + 1 ) 3 2 Equate the derivative of F ( x ) to f ( x ) as follows. F ′ ( x ) = f ( x ) d d x ( a ( 6 x + 1 ) 3 2 ) = 3 2 ( 6 x + 1 ) 1 2 ( 6 ) 3 2 a ( 6 x + 1 ) 1 2 d d x ( 6 x ) = 3 2 ( 6 x + 1 ) 1 2 ( 6 ) 3 2 a ( 6 x + 1 ) 1 2 ( 6 ) = 3 2 ( 6 x + 1 ) 1 2 ( 6 ) 9 a ( 6 x + 1 ) 1 2 = 9 ( 6 x + 1 ) 1 2 Compare the coefficient of ( 6 x + 1 ) 1 2 as, 9 a = 9 a = 1 Substitute a = 1 in the anti-derivative F ( x ) = a ( 6 x + 1 ) 3 2

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 25.1, Problem 35E

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The anti-derivative of the given function $f(x)=32(6x+1)12(6)$ .

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Chapter 25.1, Problem 34E

Chapter 25.1, Problem 36E

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Chapter 25 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 25.1 - Find an antiderivative of x3 + 4x. Ch. 25.1 - Prob. 2PE Ch. 25.1 - Prob. 1E Ch. 25.1 - Prob. 2E Ch. 25.1 - Prob. 3E Ch. 25.1 - Prob. 4E Ch. 25.1 - In Exercises 5–12, determine the value of a that...Ch. 25.1 - Prob. 6E Ch. 25.1 - Prob. 7E Ch. 25.1 - Prob. 8E

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The anti-derivative of the given function f ( x ) = 3 2 ( 6 x + 1 ) 1 2 ( 6 ) .

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