According to the question, $$ \begin{aligned} & 27 r_1+\frac{9 r_2}{2}=-9 \\ & \lim _{x \rightarrow 3} \frac{\int_3^x 8 t^2 d t}{\frac{3 r_2 x}{2}-r_2 x^2-r_1 x^3-3 x} \\ & =\lim _{x \rightarrow 3} \frac{8 x^2}{\frac{3 r_2^2}{2}-2 r_2 x-3 r_1 x^2-3} \text { (using LH' Rule) } \\ & =\frac{72}{\frac{3 r_2}{2}-6 r_2-27 r_1-3} \\ & =\frac{72}{-\frac{9 r_2}{2}-27 r_1-3} \\ & =\frac{72}{9-3}=12 \end{aligned} $$