11. (i) Find ∫(3x – x^3/2)dx.
The diagram shows part of the curve y = 3x – x^3/2 and the lines y = 3x and 2y = 27 – 3x. The curve and the line y = 3x meet the axis at O and the curve and the line 2y = 27 – 3x meet the axis at A.
(ii) Find the coordinates of A.
(iii) Verify that the coordinates of B are (3,9)
(iv) Find the area of the shaded region.