# The antiderivative of each function

### 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 64E

(A)

To determine

## To find:The antiderivative of each function

Expert Solution

2x323+c

### Explanation of Solution

Given:

The function

f(x)=x

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)=x.............(1)

if F'(x)=f(x)

Integrating the equation (1) by given the limit

xdx=2x323+c

(B)

To determine

Expert Solution

ex+2x4+c

### Explanation of Solution

Given:

The function

f(x)=ex+8x3

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)=ex+8x3.............(1)

if F'(x)=f(x)

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

ex+8x3dx=ex+8x44+cex+8x3dx=ex+2x4+c

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