If the area of the region (x, y) : x + 2, 5 - 2x y 8 - x^2 is A , then the value of 2A is

Step-by-step solution

To find the area of the region, we first determine the boundaries of the curves. The upper boundary is the parabola y = 8 - x^2 . The lower boundary is the piecewise function y = x + 2, 5 - 2x . Find the intersection of the two lines inside the max function: x + 2 = 5 - 2x 3x = 3 x = 1 . For x 1 , 5 - 2x x + 2 , so x + 2, 5 - 2x = 5 - 2x . For x 1 , x + 2 5 - 2x , so x + 2, 5 - 2x = x + 2 . Next, find the intersection points of the parabola with these lines to determine the limits of integration: For x 1 : 8 - x^2