### Home > APCALC > Chapter 2 > Lesson 2.2.3 > Problem2-84

2-84.

Write a Riemann sum for a general function $f$ to estimate the area under the curve for $2\le x\le5$ using $n$ left endpoint rectangles of equal width if:

1. $n = 3$ rectangles

1. $n = 9$ rectangles

1. $n = 300$ rectangles

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.
$b$ represents ending value on the $x$-axis.

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