​ Tìm a biết ∫a1x+1xdx=e. ​

Question

Tìm a biết \(\int _{1}^{a}\frac{x+1}{x}  dx=e.   \)

 A. \(\frac{2}{1-e}\) .  B.\( \frac{-2}{1-e}\) .  C. e. D. \(\frac{e}{2}\) . 

Answer 1

Chọn C

 Ta có: \(\int _{1}^{a}\frac{x+1}{x}  dx=\int _{1}^{a}\left(1+\frac{1}{x} \right) dx=\left. \left(x+\ln \left|x\right|\right)\right|_{1}^{a}\)

\(=a+\ln \left|a\right|-1-0=e\Rightarrow a+\ln \left|a\right|=e+1\Rightarrow a=e \)