BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 1E

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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