### Home > APCALC > Chapter 3 > Lesson 3.3.2 > Problem3-106

3-106.

Examine the Riemann sum at right for the area under $f$.

1. How many rectangles were used?

Notice that the index starts at $0$ and ends at $11$.

2. If the area being approximated is over the interval $a\le x\le b$, what are the values of $a$ and $b$?

General form of a left endpoint Riemann sum:$\displaystyle \sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

$a = 3$ is easy to spot in the Riemann sum. Now determine the end value, $b$.

Notice that $\Delta x= \frac{6-3}{12}=\frac{1}{4}$, so each rectangle has a width of $\frac{1}{4}$.

You already computed how many rectangles there are part (a).

$\displaystyle\sum _ { i = 0 } ^ { 11 } \frac { 6 - 3 } { 12 } f ( 3 + \frac { 6 - 3 } { 12 } \cdot i )$