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Câu hỏi: Cho $\int\limits_{1}^{2}{f\left( x \right)\text{d}x=-3}$, ${\int\limits_{2}^{5}{f\left( x \right)\text{d}x=5}}$ và ${\int\limits_{1}^{5}{g\left( x \right)\text{d}x=6}}$. Tính tích phân $I=\int\limits_{1}^{5}{\left[ 2.f\left( x \right)-g\left( x \right) \right]\text{d}x}$.
A. $I=-2$.
B. $I=10$.
C. $I=4$.
D. $I=8$.
Ta có $\int\limits_{1}^{2}{f\left( x \right)\text{d}x=-3}$ và $\int\limits_{2}^{5}{f\left( x \right)\text{d}x=5}$ nên $\int\limits_{1}^{5}{f\left( x \right)\text{d}x=2}$.
$I=\int\limits_{1}^{5}{\left[ 2.f\left( x \right)-g\left( x \right) \right]\text{d}x}$ $=2\int\limits_{1}^{5}{f\left( x \right)\text{d}x}-\int\limits_{1}^{5}{g\left( x \right)\text{d}x}$ $=-2$.
A. $I=-2$.
B. $I=10$.
C. $I=4$.
D. $I=8$.
Ta có $\int\limits_{1}^{2}{f\left( x \right)\text{d}x=-3}$ và $\int\limits_{2}^{5}{f\left( x \right)\text{d}x=5}$ nên $\int\limits_{1}^{5}{f\left( x \right)\text{d}x=2}$.
$I=\int\limits_{1}^{5}{\left[ 2.f\left( x \right)-g\left( x \right) \right]\text{d}x}$ $=2\int\limits_{1}^{5}{f\left( x \right)\text{d}x}-\int\limits_{1}^{5}{g\left( x \right)\text{d}x}$ $=-2$.
Đáp án A.