### Home > PC3 > Chapter 3 > Lesson 3.2.3 > Problem3-122

3-122.

Let $y=\frac{2}{x}$.

1. Divide the interval $4\le x\le6$ into five equal pieces. What is the width of each piece?

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

2. List the values of $x_0$, $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$.

$x_0=4$
Now add the width to $x_0$ to determine the location of $x_1$. Continue the same for the last two.

3. Use five rectangles to produce an underestimate for the area under the curve.

4. Next, use five rectangles to produce an overestimate for the area under the curve.

5. What change can you make so that the underestimate and overestimate are closer together?