+ + + +

J~ (x2 - x){2C2+ C3(6x - 2) + Q[Yx + C2(X2 - x) + C3(X3 - ~)]- F} dx = 0 (12.63a)

L(x3 - ~)/2C2 + C3(6x - 2) + Q[Yx + C2(X2 - x) + C3(X3 - x2)]_ F} dx = 0 (12.63b)

The functions Q = Q(x) and F = F(x) must be substituted into Eq. (12.63) before integrating. Step 6. Integrate Eq. (12.63), for Q = constant and F = constant, evaluate the results, and collect terms. The final result is

(12.64a)

(12.64b)

Equation (12.64) is identical to the result obtained by the Rayleigh-Ritz method, Eq. (12.36). This correspondence always occurs when the weighting functions

~(x) (j = I, 2, ...), are chosen as the trial functions, Yi(X).