   Chapter 4.P, Problem 8P

Chapter
Section
Textbook Problem

# Use an integral to estimate the sum ∑ i = 1 10000 i .

To determine

To estimate:

The sum

Explanation

1) Concept:

If f is integrable on a, b, then

abfxdx=limni=1nfa+i·b-anb-an

2) Given:

i=110000i

3) Calculation:

Let n=10000.

We want to rewrite i in terms of n.

By multiplying and dividing by n,

i=in·n

By multiplying and dividing by n,

=in·n·n·1n

By simplifying,

=n32·1nin

i=n32in·1n

So,i=1ni=i=1nn32in ·1n=n32i=1nin ·1n Comparing this with ab

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