### Home > CALC > Chapter 3 > Lesson 3.1.1 > Problem3-9

3-9.

Write an expression using sigma notation that represents the sum of the areas of the rectangles shown for the function below. Note, the rectangles have equal widths.

Questions to consider:

How many rectangles are there, $n$?

Are they left-endpoint, right-endpoint or midpoint rectangles?

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

Right-endpoint:
$\displaystyle\sum_{i=1}^{n}\Delta xf\left ( a+\Delta xi \right )$

Midpoint:
$\displaystyle \sum_{i=0}^{n-1}\Delta xf\left ( a+\frac{\Delta x}{2}i \right )$

What is the width/base of each rectangle, $Δx$?

$\Delta x=\frac{b-a}{n}$

What is the function?

What is the starting value, $a$?
On what interval is the area being approximated?