CPM Homework Help : APCALC Problem 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.

Increasing curve, changing from opening up to opening down at the approximate point (0, comma 2.5) & 6 shaded vertical rectangles, bottom edges on x axis, each with width, 1 third, starting at, x = negative 1, & each with top left vertex, on the curve.

Hint:

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, $\Delta x$ ?

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

What is the function?

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