### Home > APCALC > Chapter 2 > Lesson 2.3.1 > Problem2-109

2-109.

The sigma notation expressions below represents Riemann sums that calculate the area under the curve of a function, $f$, for $a\le x\le b$ using $n$ rectangles of equal width. For each summation, determine the values of $a, b,$ and $n$.

1. $\displaystyle\sum _ { i = 0 } ^ { 17 } \frac { 1 } { 3 } f ( - 6 + \frac { 1 } { 3 } i )$

1. $\displaystyle\sum _ { i = 0 } ^ { 9 } \frac { 1 } { 10 } f ( 4 + \frac { 1 } { 10 } i )$

General form of left-endpoint Riemann Sum:

$\displaystyle \sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

$n$ represents number of rectangles.
$a$ represents starting value on the $x$-axis.

$\Delta x\text{ represents width of each rectangle}:\frac{b-a}{n}$