List x1, x2, x3, x4 where xi is the right endpoint of the four equal intervals used to estimate the area under the curve of f(x) between x = 3 and x = 5.
3, 3.5, 4, 4.5
3, 3.2, 4.6, 5
3.5, 4, 4.5, 5
3.25, 3.75, 4.25, 4.75
my answer was a because i kept getting numbers like 3, 3.6, and 4.2 and a was the closest can someone check it
if xi is the right endpoint, then 3 cannot be x1. That leaves only c and d for choices.
Since the interval length is 2, and the number of divisions is 4, each interval is .5 in width.
Looks like (c) to me.
BTW, (d) is the set of midpoints.
To estimate the area under the curve of f(x) between x = 3 and x = 5 using four equal intervals, we need to divide the interval [3, 5] into four equal parts.
The width of each interval can be found by dividing the total width of the interval by the number of intervals. In this case, the total width is 5 - 3 = 2.
Therefore, the width of each interval is 2 / 4 = 0.5.
To find the right endpoint of each interval, we start with the left endpoint (in this case, x = 3) and add the width of each interval to it successively.
Using this process, we can generate the following right endpoints:
x1 = 3 + 0.5 = 3.5
x2 = 3.5 + 0.5 = 4
x3 = 4 + 0.5 = 4.5
x4 = 4.5 + 0.5 = 5
We find that the correct answer is option C: 3.5, 4, 4.5, 5.
Therefore, your initial answer was incorrect.
To estimate the area under the curve of f(x) between x = 3 and x = 5 using four equal intervals, we need to divide the interval [3, 5] into four equal parts.
The right endpoints of these intervals, denoted as x1, x2, x3, x4, can be found by incrementing the starting point by the length of each interval.
The length of each interval is given by (5 - 3) / 4 = 2 / 4 = 0.5.
Starting from x = 3, we can find the right endpoints as follows:
x1 = 3 + 0.5 = 3.5
x2 = 3.5 + 0.5 = 4
x3 = 4 + 0.5 = 4.5
x4 = 4.5 + 0.5 = 5
Therefore, the correct answer is (3.5, 4, 4.5, 5).