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 18E
To determine

To find:The limit as a defined integral on the given interval

Expert Solution

Answer to Problem 18E

Defined integral on the interval [π,2π]=π2πcosxxdx

Explanation of Solution

Given information:

  limni=1ncosxixiΔx , [π,2π]

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:

Comparing the given limit limni=1ncosxixiΔx

with

  abf(x)dx=limni=1nf(xi)Δx

Here f(x)=cosxx

And a=π

And

  b=2π

Substitute a=π and b=2π

And

  f(x)=cosxx

So, define integral on the interval [π,2π]=π2πcosxxdx

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!