Question

An example of a math question calculated using mid ordinate rule

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's say we have the following data points for a function at intervals of 1:

x = 1, 2, 3, 4, 5, 6, 7
y = 3, 5, 6, 8, 10, 12, 14

Using the mid ordinate rule, we can find the estimate of the area under the curve for these data points.

The formula for the mid ordinate rule is:

Area ≈ h * Σf(xᵢ)

where h is the width of each interval and is equal to 1 in this case, f(xᵢ) is the function value at the midpoint of each interval.

First, we need to find the midpoints:

midpoints = (1+2)/2, (2+3)/2, (3+4)/2, (4+5)/2, (5+6)/2, (6+7)/2
= 1.5, 2.5, 3.5, 4.5, 5.5, 6.5

Next, we need to find the function values at the midpoints:

f(midpoints) = 4, 5.5, 7, 9, 11, 13

Now, we can calculate the area using the mid ordinate rule formula:

Area ≈ 1 * (4 + 5.5 + 7 + 9 + 11 + 13)
Area ≈ 1 * 49.5
Area ≈ 49.5

Therefore, the estimated area under the curve using the mid ordinate rule for this set of data points is 49.5.