Biết tích phân \({I_1} = \i...

B

- Hướng dẫn giải

\({I_1} = \int\limits_{\frac{\pi }{3}}^{\frac{\pi }{2}} {\sin xdx} = \left. {\left( {\cos x} \right)} \right|_{\frac{\pi }{3}}^{\frac{\pi }{2}} = \frac{1}{2}\)

\(\begin{array}{l} \Rightarrow {I_2} = \int\limits_a^1 {\frac{{{x^2} + 1}}{{{x^3} + x}}dx} = \int\limits_{\frac{1}{2}}^1 {\frac{{{x^2} + 1}}{{{x^3} + x}}dx} \\ = \frac{1}{3}\left. {\left( {\ln \left| t \right|} \right)} \right|_{\frac{5}{8}}^2 = \frac{4}{3}\ln 2 - \frac{1}{3}\ln 5\\ \Rightarrow b = \frac{4}{3},c = - \frac{1}{3} \Rightarrow \frac{b}{c} = - 4\end{array}\)