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.
each interval has width 2, so the midpoints are at 1,3,5,7,9
1, 3, 5, 7, 9 is the correct answer.
To find the midpoints of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10, follow these steps:
Step 1: Calculate the interval size. The interval size can be found by dividing the total interval range (10 - 0 = 10) by the number of intervals (5). Therefore, the interval size is 10/5 = 2.
Step 2: Find the midpoint of each interval. To find the midpoint, you add half of the interval size to the starting point of each interval.
For the first interval (interval 1), the starting point is 0. Adding half of the interval size (2/2 = 1) gives us x1 = 0 + 1 = 1.
For the second interval (interval 2), the starting point is 2. Adding half of the interval size (2/2 = 1) gives us x2 = 2 + 1 = 3.
For the third interval (interval 3), the starting point is 4. Adding half of the interval size (2/2 = 1) gives us x3 = 4 + 1 = 5.
For the fourth interval (interval 4), the starting point is 6. Adding half of the interval size (2/2 = 1) gives us x4 = 6 + 1 = 7.
For the fifth interval (interval 5), the starting point is 8. Adding half of the interval size (2/2 = 1) gives us x5 = 8 + 1 = 9.
Therefore, the midpoints of the five equal intervals are x1 = 1, x2 = 3, x3 = 5, x4 = 7, and x5 = 9.
To find the midpoint endpoints of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10, we need to divide the interval [0, 10] into five equal parts.
The width of each interval will be (10 - 0) / 5 = 2.
To find the midpoint of each interval, we can use the formula: xi = (a + b) / 2, where xi is the midpoint, a is the lower bound of the interval, and b is the upper bound of the interval.
Let's calculate the values of x1, x2, x3, x4 using this formula:
For the first interval:
a = 0 (lower bound)
b = a + width = 0 + 2 = 2 (upper bound)
x1 = (0 + 2) / 2 = 1 (midpoint)
For the second interval:
a = 2 (lower bound)
b = a + width = 2 + 2 = 4 (upper bound)
x2 = (2 + 4) / 2 = 3 (midpoint)
For the third interval:
a = 4 (lower bound)
b = a + width = 4 + 2 = 6 (upper bound)
x3 = (4 + 6) / 2 = 5 (midpoint)
For the fourth interval:
a = 6 (lower bound)
b = a + width = 6 + 2 = 8 (upper bound)
x4 = (6 + 8) / 2 = 7 (midpoint)
Therefore, the values of x1, x2, x3, x4 are 1, 3, 5, and 7 respectively.