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 28E
To determine

To express the integral as a limit of Riemann sum.

Expert Solution

Answer to Problem 28E

The value of Riemann sum is limxi=1n[(1+9ni)4ln(1+9ni)]9n .

Explanation of Solution

Given information:

The equation is

  110(x4lnx)dx

The given expression can be obtained as

  110(x4lnx)dx

The width of the subintervals is

  Δx=banΔx=101n          [since, b=10,a=1]Δx=9n

And

  xi=a+iΔxxi=1+9ni                 [since, a=1,Δx=9n]

Therefore,

  110(x4lnx)dx=limxi=1nf(xi)Δx

Put the values of Δx=9n,xi=1+9ni on the above equation

  110(x4lnx)dx=limxi=1nf(xi)Δx                          =limxi=1n[(1+9ni)4ln(1+9ni)]9n

Hence,

The value of Riemann sum is limxi=1n[(1+9ni)4ln(1+9ni)]9n .

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