The total area of the regions between the curves is 13.83 square units
Calculating the total area of the regions between the curves
From the question, we have the following parameters that can be used in our computation:
y = -(1/9)x² + 6, y = √(x-2), y = 2-x,
With the use of graphs, the curves intersect at
x = -3 and x = 6
So, the area of the regions between the curves is
Area = ∫-(1/9)x² + 6 - √(x-2) - 2 + x
This gives
Area = ∫-(1/9)x² + 4 - √(x-2) + x
Integrate

Using the limits, we have
So, we have
Area = 83/6
Evaluate
Area = 13.83
Hence, the total area of the regions between the curves is 13.83 square units