# To express the limit as a definite integral.

### 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 54E
To determine

## To express the limit as a definite integral.

Expert Solution

The definite integral is limx(1n)i=1n11+(in)2=01(11+x2)dx .

### Explanation of Solution

Given information:

The equation is

limx(1n)i=1n11+(in)2

Formula used:

abf(x)dx=limxΔxi=1nf(a+iΔx)where Δx=ban

The given expression can be express as

limx(1n)i=1n11+(in)2=limxi=1n11+(in)2(1n)=limx(1n)i=1n11+(0+i(1n))2

Compare the above equation to the formula,

Δx=1n,a=0 and f(x)=(11+x2)

Find b ,

Δx=ban1n=b0nb=1

Therefore,

limx(1n)i=1n11+(in)2=01(11+x2)dx

Hence,

The definite integral is limx(1n)i=1n11+(in)2=01(11+x2)dx .

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