Cho hàm số \(f\left( x \right)\) liên tục trên \(\mathbb{R}\) và \(\int\limits_{0}^{1}{\left[ f\left( x \right)+3{{x}^{2}} \right]\text{d}x}=6\). Khi đó \(\int\limits_{0}^{1}{f\lef...

* Hướng dẫn giải

Ta có \(\int\limits_{0}^{1}{\left[ f\left( x \right)+3{{x}^{2}} \right]\text{d}x}=6 \Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{0}^{1}{3{{x}^{2}}\text{d}x}=6 \Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\left. {{x}^{3}} \right|_{0}^{1}=6\)

\(\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\left( 1-0 \right)=6 \Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}=5\).