(a) If \(f(x) = \int (4x - x^{2}) \mathrm {d} x\) and f(3) = 21, find f(x). (b) The second, fourth and eigth terms of an Arithmetic Progression (A.P) form t...

(a) If \(f(x) = \int (4x - x^{2}) \mathrm {d} x\) and f(3) = 21, find f(x).

(b) The second, fourth and eigth terms of an Arithmetic Progression (A.P) form the first three consecutive terms of a Geometric Progression (G.P). The sum of the third and fifth terms of the A.P is 20, find the :

(i) first four terms of the A.P

(ii) sum of the first ten terms of the A.P