Question

Find the area of the region bounded by the curve y² = 2y – x and the y-axis.

Answer 1

 

Given curve is

Obviously, given curve is left handed parabola having vertex at (1, 1).

Putting x = 0 in (i), we get

y² = 2y ⇒ y(y - 2) = 0 ⇒ y = 0, 2

i.e., given parabola meets y axis at y = 0 and y = 2, so shaded region is required region.

\(\therefore\) Required area = Area of region OABO