# The limit as a defined integral on the given interval

### 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 5.2, Problem 18E
To determine

## To find:The limit as a defined integral on the given interval

Expert Solution

Defined integral on the interval [π,2π]=π2πcosxxdx

### Explanation of Solution

Given information:

limni=1ncosxixiΔx , [π,2π]

Concept Used:

If f(x) is integrableon [a,b] , then

abf(x)dx=limni=1nf(xi)Δx

Where Δx=ban and xi=a+iΔx

Calculation:

Comparing the given limit limni=1ncosxixiΔx

with

abf(x)dx=limni=1nf(xi)Δx

Here f(x)=cosxx

And a=π

And

b=2π

Substitute a=π and b=2π

And

f(x)=cosxx

So, define integral on the interval [π,2π]=π2πcosxxdx

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