# 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 53E
To determine

## To express the limit as a definite integral.

Expert Solution

The value of definite integral is limxi=1ni4n5=01x4dx=15 .

### Explanation of Solution

Given information:

The equation is

limxi=1ni4n5

Formula used:

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

The given expression can be express as

limxi=1ni4n5=limxi=1ni4n4(1n)=limx(1n)i=1n(0+1ni)4

Compare the above equation to the formula,

Δx=1n,a=0 and f(x)=x4

Find b ,

Δx=ban1n=b0nb=1

Therefore,

limxi=1ni4n5=01x4dx=15

Hence,

The value of definite integralis limxi=1ni4n5=01x4dx=15 .

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