   Chapter 4.9, Problem 8E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the most general antiderivative of the function. (Check your answer by differentiation.) f ( x ) = x 3 , 4 − 2 x 2 − 1

To determine

To find: The most general antiderivative of the function f(x)=x3.42x21 and check the determined antiderivative for the function f(x)=x3.42x21 by differentiation.

Explanation

Given Data:

Write the given function as follows.

f(x)=x3.42x21

Formula used 1:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

Formula used:

Write the required differentiation formula to verify the answer as follows.

ddx(xn)=nxn1ddx(constant)=0

Calculation:

Write the function as follows.

f(x)=x3.42x21 (1)

From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows.

F(x)=x3.4+13.4+12(x21+121+1)+C=x4.44.42(x22)+C=14.4x4.42x2+C=1044x4.42x2+C

F(x)=522x4.42x2+C

Thus, the most general antiderivative of the function f(x)=x3.42x21 is 522x4.42x2+C_

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Study Guide for Stewart's Multivariable Calculus, 8th 