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.

Question

Question options:

1)	2, 4, 6, 8, 10
2)	1, 3, 5, 7, 9
3)	0, 2, 4, 6, 8
4)	1, 2, 3, 4, 5

Answer 1

Take a piece of graph paper and draw a number line from 0 to 10 on the x-axis. Now, imagine chopping up this line into 5 equal intervals. How many units wide must each interval be? Two units!

Your intervals are:

0 to 2

2 to 4

4 to 6

6 to 8

8 to 10

The midpoint or middle of each interval is 1, 3, 5, 7, 9.

Side note:

If you were asked for the right endpoint, you would use 2, 4, 6, 8, 10

If asked for the left endpoint, you would use 0, 2, 4, 6, 8