### Home > PC3 > Chapter 13 > Lesson 13.2.1 > Problem13-62

13-62.

Suppose you want to approximate the area under the curve of a function $f$ over the interval $1\le x\le10$ using $25$ sub-intervals.

1. What is the width of each rectangle?

$\text{width }=\frac{\text{length of interval}}{\text{number of rectangles}}$

2. What will be the height of the first rectangle be if left endpoint rectangles are used?

$x_{0} = ? →$ height of rectangle $= f\left(x_{0}\right)$

3. What will be the height of the first rectangle be if right endpoint rectangles are used?

$f\left(x_{1}\right)$

4. What will be the height of the last rectangle be if left endpoint rectangles are used?

Left endpoints go from $x_{0}$ to $x_{n−1}$.
$f(x_{n-1})$

5. What will be the height of the last rectangle be if right endpoint rectangles are used?

$f\left(x_{n}\right)$

6. How would your answers change if the interval were $B\le x\le E$ and the width of each rectangle were $W$?