# Whether the statement, the most general antiderivative of f ( x ) = x − 2 is F ( x ) = − 1 x + C is true or false.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 18RQ
To determine

## Whether the statement, the most general antiderivative of f(x)=x−2 is F(x)=−1x+C is true or false.

Expert Solution

The given statement is false.

### Explanation of Solution

The given function is, f(x)=x2 .

Integrate the given function and obtain the antiderivative of f(x) as follows.

F(x)=x2dx=x2+12+1+C=x11+C=1x+C

Thus, the antiderivative is 1x+C .

Therefore, the given statement is false.

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