# The significance of anti derivative of a 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 4, Problem 10RCC

a.

To determine

## The significance of anti derivative of a function

Expert Solution

### Explanation of Solution

Anti derivative is used to find a function F whose derivative is f and is a known function.

According to the definition,

A function F is called an anti derivative of f on interval l if

F'(x)=f(x)for all x in l.

Now let,

f(x)=cosx

Then the anti derivative of f(x) is,

F=sinx+c.

b.

To determine

Expert Solution

### Explanation of Solution

Anti derivative is used to find a function F whose derivative is f and is a known function.

According to the definition,

A function F is called an anti derivative of f on interval l if

F'(x)=f(x)for all x in l.

Now if both F1 and F2 are anti derivative of f then we can write,

f=ddx(F1+c1)and,f=ddx(F2+c2)

Thus we can see that for different values of c1 and c2 both F1 and F2 are anti derivative of f .

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