   Chapter 4.9, Problem 11E ### 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 ) = 3 x − 2 x 3

To determine

To find: The most general antiderivative of the function f(x)=3x2x3 and check determined antiderivative for the function f(x)=3x2x3 by differentiation.

Explanation

Given Data:

Write the given function as follows.

f(x)=3x2x3

Formula used 1:

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

Here, C is the constant.

Formula used 2:

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

ddx(xn)=nxn1ddx(constant)=0

Calculation:

Rewrite the function f(x)=3x2x3 as follows.

f(x)=3x122x13 (1)

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

F(x)=3(x12+112+1)2(x13+113+1)+C=3(x3232)2(x4343)+C=2x3232x43+C

Thus, the most general antiderivative of the function f(x)=3x2x3 is 2x3232x43+C_ .

Here the determined antiderivative for the function f(x)=3x2x3 is 2x3232x43+C

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 