# The limit as a defined integral on the given interval

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 5.2, Problem 17E
To determine

Expert Solution

## Answer to Problem 17E

Defined integral on the interval [2,6]=

26xln(1+x2)dx

### Explanation of Solution

Given information:

limni=1nxiln(1+xi2)Δx , [2,6]

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=1nxiln(1+xi2)Δx

with

abf(x)dx=limni=1nf(xi)Δx

Here f(x)=xln(1+x2)

And a=2 and b=6

Substitute a=2 and b=6 and f(x)=xln(1+x2)

So, define integral on the interval [2,6]=

26xln(1+x2)dx

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