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Câu hỏi: 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 $\int\limits_{0}^{1}{f\left( x \right)\text{d}x}$ bằng
A. $0$.
B. $5$.
C. $3$.
D. $9$.
A. $0$.
B. $5$.
C. $3$.
D. $9$.
Ta có $\int\limits_{0}^{1}{\left[ f\left( x \right)+3{{x}^{2}} \right]\text{d}x}=6$ $\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\int\limits_{0}^{1}{3{{x}^{2}}\text{d}x}=6$ $\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\left. {{x}^{3}} \right|_{0}^{1}=6$
$\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\left( 1-0 \right)=6$ $\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}=5$.
$\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}+\left( 1-0 \right)=6$ $\Leftrightarrow \int\limits_{0}^{1}{f\left( x \right)\text{d}x}=5$.
Đáp án B.