Question

A curve has a parametric equation x=〖at〗^2 and y=2at. If the area is bounded by the curve between t=1 and t=2

Answer 1

If you mean the area under the curve, that is, as usual,
∫ y dx = ∫[1,2] 2at * (2at * 2a) dt = ∫[1,2] 8a^3 t^2 dt = 56/3 a^3

Answer 2

oops. did you see my typo? Better fix it.