2.1: Area bounded by a curve and two straight lines

The diagram shows part of the curve $y = 3x - x^{\frac{3}{2}}$ and the lines $y = 3x$ and $2y = 27 - 3x$. The curve and the line $y = 3x$ meet the $x$-axis at $O$ and the curve and the line $2y = 27 - 3x$ meet the $x$-axis at $A$.