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 27E
To determine

To express the integral as a limit of Riemann sum.

Expert Solution

Answer to Problem 27E

The value of Riemann sum is limxi=1n[(2+4ni)1+(2+4ni)5]4n .

Explanation of Solution

Given information:

The equation is

  26x1+x5dx

The given expression can be obtained as

  26x1+x5dx

The width of the subintervals is

  Δx=banΔx=62n          [since, b=6,a=2]Δx=4n

And

  xi=a+iΔxxi=2+4ni                 [since, a=2,Δx=4n]

Therefore,

  26x1+x5dx=limxi=1nf(xi)Δx

Put the values of Δx=4n,xi=2+4ni on the above equation

  26x1+x5dx=limxi=1nf(xi)Δx                  =limxi=1n[(2+4ni)1+(2+4ni)5]4n

Hence,

The value of Riemann sum is limxi=1n[(2+4ni)1+(2+4ni)5]4n .

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