The area of the region that lies to the right of the y axis and to the left of the parabola x 2y y 2 (the shaded region in the figure) is given by the integral 2 0 (2y y 2 ) dy (Turn your head clockwise and think of the region as lying below the curve x 2y y 2 from y 0 to y 2 ) Find the area of the...

The area of the region that lies to the right of the y-axis and to the left

Question:

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 ∫²₀(2y – y²) 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.