Denoting the areas of the three strips by A, B, and C, and introducing the middle ordinate ug, we can express A + B; B -{- C; A + B -FC; and B in terms of uo, u 1, u 2; u 1, u2, u3; uo, u, u 3; and u 1, ug, u 2 respectively.
(i) If m is even, ug m will be onejof the given ordinates, and we can express h 2 u, m, 4 u" m, ...
denote 2 (ug 'm _ z + ug m+ g), ?
Thus we get two expressions for A + B -}- C, from which we can eliminate ug.
The breadth of the trapezette being mh, it may be shown that its area is 2 2 N 4 4 iv I mh ug m + 24 m h u gm + 1920 m h u g m + 322560 no/tourgm -}- m3l1gu i„?