The enclosed area between the curves y=(x−2)2𝑦=(𝑥−2)2 and y=−2x+4𝑦=−2𝑥+4 is

To find the enclosed area between the curves y=(x−2)² and y=−2x+4, we need to follow these steps:

1. First, we need to find the points of intersection of the two curves. We do this by setting the two equations equal to each other and solving for x:

   (x-2)² = -2x + 4

   Expanding and simplifying gives us:

   x² - 4x + 4 = -2x + 4

   Simplifying further gives:

   x² - 2x = 0

   Factoring out an x gives:

   x(x - 2) = 0

   Setting each factor equal to zero gives the solutions x = 0 and x = 2.

2. Next, we set up the integral to find the area between the curves. We subtract the lower function (y = (x-2)²) from the upper function (y = -2x + 4) and integrate from the left point of intersection (x = 0) to the right point of intersection (x = 2):

   ∫ from 0 to 2 [-2x + 4 - (x-2)²] dx

3. Evaluating this integral will give us the area between the curves.

Please note that the integral calculation can be complex and may require knowledge of calculus to solve.