y = x - 2 x +1 + x 4 y = 5 - x For the given figure, notice that the shaded region is in the interval [0, 4]); however, neither graph lies above the other over this entire interval. It appears that the lines intersect at x = 2, but this should be confirmed algebraically. To find the x-coordinates of the intersection points, set the equations y = x2 - 2x + 1 and y = 5 - x² equal to each other and solve for x as follows. x2 - 2x + 1 = 5 - x2 2x2 - 2x – 4 = 0 collect like terms x2 - x - 2 = o divide by 2 (x + 1) = 0 factor x + 1 = 0 or x - 2 = 0 set each factor equal to zero x = -1 or x = solve for x Since x = -1 is not in the interval [0, 4], this solution is discarded. The solution x = the x-coordinate of the intersection point of the two graphs in the interval [0, 4]. gives us We can now apply the area formula above if we split the interval [0, 4] into two intervals, one from [0, 2] and the other from