Chapter 4.4, Problem 45E

The area of the region that lies to the right of the y-axis and to the left of the parabola x = 2y – y² (the shaded region in the figure) is given by the integral ${\displaystyle {\int }_0^2\left(2y-y^2\right)dy}$. (Turn your head clockwise and think of the region as lying below the curve x = 2y – y² from y = 0 to y = 2.) Find the area of the region.