Chapter 11.2, Problem 14E

Solution

To find: The eight subintervals of the interval $\left[0,2\right]$ .

The eight subintervals between $\left[0,2\right]$ are $s=\left\{\left(0,\frac{1}{4}\right)\left(\frac{1}{4},\frac{1}{2}\right)\left(\frac{1}{2},\frac{3}{4}\right)\left(\frac{3}{4},1\right)\left(1,\frac{5}{4}\right)\left(\frac{5}{4},\frac{3}{2}\right)\left(\frac{3}{2},\frac{7}{4}\right)\left(\frac{7}{4},2\right)\right\}$ .

Given information:

Interval $\left[0,2\right]$ .and number of subintervals which is $4$

Formula used:

  $\Delta x=\frac{b-a}{n}$

Here, $\left[a,b\right]=\left[0,2\right]$ and $n=8$

Calculation:

Substitute the values of $a$ , $b$ and $n$ . In the formula,$\begin{array}{c}\Delta x=\frac{2-0}{8}\\ =\frac{1}{4}\end{array}$

Starting with $a$ , add $\Delta x$ to obtain the endpoint of the subinterval. The endpoint of the previous subinterval is the starting point of the next and repeat the process

So, the eight subintervals of interval $\left[0,2\right]$ are $s=\left\{\left(0,\frac{1}{4}\right)\left(\frac{1}{4},\frac{1}{2}\right)\left(\frac{1}{2},\frac{3}{4}\right)\left(\frac{3}{4},1\right)\left(1,\frac{5}{4}\right)\left(\frac{5}{4},\frac{3}{2}\right)\left(\frac{3}{2},\frac{7}{4}\right)\left(\frac{7}{4},2\right)\right\}$ .