Biết \(I_{1}=\int_{\frac{\p...

B

- Hướng dẫn giải

Ta có:

\(\begin{array}{l} I_{1}=\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \sin x d x=\left.(\cos x)\right|_{\frac{\pi}{3}} ^{\frac{\pi}{2}}=\frac{1}{2} \\ \Rightarrow I_{2}=\int_{a}^{1} \frac{x^{2}+1}{x^{3}+x} d x=\int_{\frac{1}{2}}^{1} \frac{x^{2}+1}{x^{3}+x} d x=\left.\frac{1}{3}(\ln |t|)\right|_{\frac{5}{8}} ^{2}=\frac{4}{3} \ln 2-\frac{1}{3} \ln 5 \Rightarrow b=\frac{4}{3}, c=-\frac{1}{3} \Rightarrow \frac{b}{c}=-4 \end{array} \)