- #1

- 143

- 0

## Homework Statement

The following sum

[tex]\sqrt{9 - \left(\frac{3}{n}\right)^2} \cdot \frac{3}{n} + \sqrt{9 - \left(\frac{6}{n}\right)^2} \cdot \frac{3}{n} + \ldots + \sqrt{9 - \left(\frac{3 n}{n}\right)^2} \cdot \frac{3}{n}[/tex]

is a right Riemann sum for the definite integral. Solve as n->infinity

[tex]\int_0^b f(x)\, dx[/tex]

## Homework Equations

[tex]\int_0^b f(x)\, dx[/tex]

## The Attempt at a Solution

I can't seem to get this one. My work is a bit long to show but I get

(9/n^3) *Sigma(i=1,n) [sqrt(n^2+i^2)]

not sure what to do here, do i substitute Sigma(i=1,n)(i^2=(n(n+1))/2?c

Last edited: