# The Riemann sum with n = 6

### 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 2E
To determine

## To Find: The Riemann sum with n=6

Expert Solution

Riemann sum of f(x) with n=6 is 0.875

### Explanation of Solution

Given information:

f(x)=x22x,0x3 with n=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:

With n=6 the interval width is

Δx=banΔx=306Δx=12xi=a+iΔx

And the right end points are

x1=0.5,x2=1,x3=1.5,x4=2,x5=2.5,x6=3

So, the Riemann Sum is

R6=i=16f(xi)ΔxR6=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx+f(x5)Δx+f(x6)ΔxR6=f(0.5)Δx+f(1)Δx+f(1.5)Δx+f(2)Δx+f(2.5)Δx+f(3)ΔxR6=0.875

Riemann sum of f(x) with n=6 is 0.875

The graph is shown below:

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