Google
Câu hỏi: Nếu $\int\limits_{0}^{\ln 3}{\left[ f\left( x \right)+{{e}^{x}} \right]} \text{dx} \text{=} \text{6}$ thì $\int\limits_{0}^{\ln 3}{f\left( x \right) \text{dx}}$ bằng
A. $6+\ln 3$.
B. $6-\ln 3$.
C. $4$.
D. $8$
A. $6+\ln 3$.
B. $6-\ln 3$.
C. $4$.
D. $8$
Ta có $\int\limits_{0}^{\ln 3}{\left[ f\left( x \right)+{{e}^{x}} \right]} \text{dx} \text{=} \text{6}\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}+\int\limits_{0}^{\ln 3}{{{e}^{x}}\text{dx}}=6\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}+\left. {{e}^{x}} \right|_{ 0}^{ \ln 3}=6$
$\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}+{{e}^{\ln 3}}-{{e}^{0}}=6\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}=4$.
$\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}+{{e}^{\ln 3}}-{{e}^{0}}=6\Leftrightarrow \int\limits_{0}^{\ln 3}{f\left( x \right)\text{dx}}=4$.
Đáp án C.