Explanation Given Data: Write the given function as follows. f ( x ) = 7 x 2 5 + 8 x − 4 5 Formula used 1: The antiderivative function for the function x n is x n + 1 n + 1 + C . Here, C is the constant. Formula used 2: Write the required differentiation formula to verify the answer as follows. d d x ( x n ) = n x n − 1 d d x ( c o n s tan t ) = 0 Calculation: Write the function as follows. f ( x ) = 7 x 2 5 + 8 x − 4 5 (1) From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows. F ( x ) = 7 ( x 2 5 + 1 2 5 + 1 ) + 8 ( x − 4 5 + 1 − 4 5 + 1 ) + C = 7 ( x 7 5 7 5 ) + 8 ( x 1 5 1 5 ) + C = 5 x 7 5 + 40 x 1 5 + C Thus, the most general antiderivative of the function f ( x ) = 7 x 2 5 + 8 x − 4 5 is 5 x 7 5 + 40 x 1 5 + C _ . Here the determined antiderivative for the function f ( x ) = 7 x 2 5 + 8 x − 4 5 is 5 x 7 5 + 40 x 1 5 + C

Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

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Author: James Stewart

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Chapter 4.7, Problem 3E

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To find: The most general antiderivative of the function f(x)=7x25+8x−45 and check the determined antiderivative for the function f(x)=7x25+8x−45 by differentiation.

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Chapter 4.7, Problem 2E

Chapter 4.7, Problem 5E

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Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

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The most general antiderivative of the function f ( x ) = 7 x 2 5 + 8 x − 4 5 and check the determined antiderivative for the function f ( x ) = 7 x 2 5 + 8 x − 4 5 by differentiation .

Solution Summary: The author explains how to find the most general antiderivative of the function f(x)=7

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To find: The most general antiderivative of the function f(x)=7x25+8x−45 and check the determined antiderivative for the function f(x)=7x25+8x−45 by differentiation.

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Chapter 4 Solutions