What is the area of the region bounded by the curve $x = y^2$, the $y$-axis and the lines $y = 1$ and $y = 2$?

Explanation

1. 01

   The region is between the curve and the $y$-axis, so integrate along $y$: Area $= \int_1^2 x\,dy = \int_1^2 y^2\,dy$.

2. 02

   $= \frac{8}{3} - \frac{1}{3} = \frac{7}{3}$ square units.