Finding Lower Sums for a Region

[ourob0ros]

Homework Statement

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!

Homework Equations

None that I'm aware of...

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?

 

[ourob0ros]

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


m_i= 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}