By symmetry
$R_1 = R_2 = \frac{1}{2}(400)(3)$
$R_1 = R_2 = 600 \, \text{lb}$
and
$(Area_{AB})\,\bar{X}_A = (Area_{AB})\,\bar{X}_B$
$(Area_{AB})\,\bar{X}_A = \frac{1}{2}(5)(1500)(\frac{5}{2}) - \frac{1}{3}(3)(450)(\frac{5}{2})$ answer
$(Area_{AB})\,\bar{X}_A = 8\,250 \text{lb}\cdot\text{ft}^3$
Thus,
$(Area_{AB})\,\bar{X}_B = 8\,250 \text{lb}\cdot\text{ft}^3$ answer