Answer:
Area of the pool = 177.6 m^2
Step-by-step explanation:
Every measure in the pool can be seen as a value of a function f(x)
The distance between each measure is represented in variable x
The pool is 24 m long (8 intervals of 3 meters each)
At the beginning and the end of the pool (x = 0 and x = 24) the function is equal to zero
n = 4 means that we have to use only 4 intervals. Using points a2, a4, a6 and a8 we get
x | 0 | 6 | 12 | 18 | 24 |
f(x) | 0 | 10.8 | 8.4 | 7.2 | 0 |
The simpson's rule states that the integral of the function, i.e. the are S of the pool, can be approximated as follows:
Area = (Δx/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)]
Replacing with Δx = 6 and the values of the function we get:
Area = (6/3)[0+ 4(10.8) + 2(8.4) + 4(7.2) + 0] = 177.6 m^2