CPM Homework Help : PC Problem 6-64

Estimate $A(f(x) = \frac { 1 } { x },1 ≤ x ≤ 5)$ using $8$ midpoint rectangles. Use sigma notation to show the sum of the areas.

Step 1:

Determine the width of each rectangle.

Answer:

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

Step 2:

Find the midpoint for each rectangle.

Answer:

$x_{0} = 1.25, x_{1} = 1.75, ...$

Step 3:

Use sigma notation to show the sum of the areas of the $8$ rectangles.

Answer:

$\displaystyle \sum_{n=0}^{7}\frac{1}{\text{(expression for }x_n\text{s})}$