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 54E
To determine

To express the limit as a definite integral.

Expert Solution

Answer to Problem 54E

The definite integral is limx(1n)i=1n11+(in)2=01(11+x2)dx .

Explanation of Solution

Given information:

The equation is

  limx(1n)i=1n11+(in)2

Formula used:

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

The given expression can be express as

  limx(1n)i=1n11+(in)2=limxi=1n11+(in)2(1n)=limx(1n)i=1n11+(0+i(1n))2

Compare the above equation to the formula,

  Δx=1n,a=0 and f(x)=(11+x2)

Find b ,

  Δx=ban1n=b0nb=1

Therefore,

  limx(1n)i=1n11+(in)2=01(11+x2)dx

Hence,

The definite integral is limx(1n)i=1n11+(in)2=01(11+x2)dx .

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!