# The coordinate line , its position at time t

### 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 3.1, Problem 63E

(A)

To determine

## To find:The coordinate line , its position at time t

Expert Solution

x33+c

### Explanation of Solution

Given:

The function

f(x)=x2

F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=x2.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

x2dx=x33+c

(B)

To determine

Expert Solution

x44+c,x55+c

### Explanation of Solution

Given:

The function

f(x)=x3,x4

F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=x3,x4.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

x3dx=x44+cx4dx=x55+c

(C)

To determine

Expert Solution

xn+1n+1+c

### Explanation of Solution

Given:

The function

f(x)=xn

F'(x)=f(x)

Concept used:

Antiderivative :- A function F(x) is antiderivative of on an interval I if F'(x)=f(x) for all x in interval I

The entire family of antiderivative of a function by adding a constant to a known antiderivative

So, if F(x) is the antiderivative of f(x) , then the family of the antiderivatives would be F(x)+c

Calculation:

The function f(x)=xn.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit of t

xndx=xn+1n+1+c

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