### Home > PC > Chapter 2 > Lesson 2.3.3 > Problem2-101

2-101.

Given $y=\frac{2}{x}$ for $4\le x\le6$

1. Divide the interval $[4,6]$ into $5$ equal pieces. What is the width of each rectangle?

$\frac{\text{interval length}}{\text{number of pieces}}$

2. Find $x_{0}$, $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, and $x_{5}$.

$x_{0} = 4$
Now add the width to $x_{0}$ to find $x_{1}$. Continue the same for the last two.

3. Use 5 rectangles to get upper and lower bounds for the area under the curve.

Review homework problem 2-98 for the process.

4. What minor change could you make to part (a) to make the upper and lower bounds closer together?

Review homework problem 2-98.