Homework Help: Finding Lower Sums for a Region

1. Jan 21, 2010

ourob0ros

1. The problem statement, all variables and given/known data

FIND THE LOWER SUM FOR THE REGION BOUNDED BY f(x) = 25 - x^2 AND THE X - AXIS BETWEEN x = 0 and x = 5. SOLVE ANALYTICALLY!!

2. Relevant equations

None that I'm aware of...

3. The attempt at a solution

f(x) = -x2 + 25
and
$$\Delta$$X = b-a/n = 5-0/n = 5/n

Here's my question: how do I find the left endpoints in order to solve for the lower sum?

Last edited: Jan 21, 2010
2. Jan 21, 2010

ourob0ros

Okay, here's what I have thus far, and I'm not sure this is correct:

mi= 5(i-1)/n

After much sigma notation and algebra...

eventually ending up with 125/n3 {(n(n+1)(2n+1)/6) - 2[n(n+1)/2] + n}