Question

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.

Answer 1

`\bf x_1 = 2\\x_2 = 4\\x_3=6\\x_4=8`

Explanation:

The given interval : x = 0 to x = 10

Length of interval = 10 - 0

= 10

`\text{Now, each }x_i \text{ is midpoint and endpoint of the five equal intervals}`

⇒ Number of equal intervals = 5

`\textbf{Length of each interval = }(10)/(5)`

`\textbf{Therefore, }\bf x_1 = 0 + 2 = 2\\x_2 = 2 +2 =4\\x_3=4+2=6\\x_4=6+2=8`