(* Enter (7.6)-(7.8) and (7.18) *)
Area0 = t - a; Area1 = (t^2 - a^2)/2;
Area2 = (t^3 - a^3)/3;Area3 = (t^4 - a^4)/4;
(* Enter (5) *)
Area = c0 Area0 + c1 Area1 + c2 Area2 + c3 Area3;
(* Enter (7.2) and a = 0.05 *)
c0 = -2450/3; c1 = 192500/9; c2 = - 980000/9; c3 = 1400000/9; a = 1/20;
Area
Simplify[Area]