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The image below shows part of a curve given by the parametric equations

\begin{aligned} x & = 3 t^{2} \\ y & = 2 t^{2} - 4 t \end{aligned}

Find the total shaded area in the diagram.

Find the coordinates of $Q$ by setting $y = 0$ .

Find the coordinates of $P$ by setting $y = 6$ .

You will have to think about which values of $t$ and $x$ actually give you $P$ and $Q$ , as the above equations will give you more than one possibility.

Split the shape into three pieces:

Find $A, B$ and $C$ separately, and add them together to find the solution.

Give your answer below.