# An antiderivative of f .

### 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 2, Problem 17RCC

(a)

To determine

## To find:An antiderivative of f .

Expert Solution

An antiderivative of f(x) is F .

### Explanation of Solution

Calculation:

Let’s f(x) be a function.

F'=f

If the function F exists, F is known as antiderivative of f(x) .

Therefore, an antiderivative of f(x) is F .

(b)

To determine

### To find:The antiderivative of velocity and acceleration function.

Expert Solution

The antiderivative of velocityfunction is the position function f(t) and the antiderivative of acceleration function is the position function v(t) .

### Explanation of Solution

Calculation:

Using for velocity v(t)=f'(t) .

The antiderivative of a velocity function is the position function f(t) .

Using for acceleration a(t)=v'(t) .

The antiderivative of a acceleration function is the position function v(t) .

Therefore, the antiderivative of velocityfunction is the position function f(t) and the antiderivative of acceleration function is the position function v(t) .

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