   Chapter 4.2, Problem 74E

Chapter
Section
Textbook Problem

# Express the limit as a definite intergal. lim n →   ∞ 1 n ∑ i = 1 n 1 1 + ( i / n ) 2

To determine

To express:

The given limit as a definite integral

Explanation

1) Concept:

Theorem:

If is f is integrable on [a, b], then

abfxdx=limni=1nfxi x

Where x= b-an and xi=a+i x

2) Given:

limn1ni=1n11+in2

3) Calculation:

Rearranging the terms

limn1ni=1n11+in2=limni=1n11+in2·1n

=limni=1n11+

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