# The differentiation and integration are inverse process. ### 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 5.4, Problem 1E
To determine

## To explain: The differentiation and integration are inverse process.

Expert Solution

The statement is correct.

### Explanation of Solution

Show the Fundamental theorem of calculus as below:

g(x)=axf(t)dt (1)

g(x)=f(x) (2)

The theorem is valid if the function f is continuous on [a,b].

Compare Equation (1) and (2).

g(x)=axf(t)dtg(x)=ddxaxf(t)dt (3)

Apply Equation (3) in (2).

g(x)=ddxaxf(t)dt=f(x)

Consider the procedure as follows:

• Integrate the function f.
• Differentiate the result of integration of f.

The original function f(x) is get back again after differentiating the result of integration of f.

Therefore, the differentiation and integration are inverse processes.

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