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Câu hỏi: Biết $\int\limits_{1}^{8}{f\left( x \right)\text{d}x}=-2;\int\limits_{1}^{4}{f\left( x \right)\text{d}x}=3;\int\limits_{1}^{4}{g\left( x \right)\text{d}x}=7$. Mệnh đề nào sau đây sai?
A. $\int_{1}^{4}[f(x)+g(x)] \mathrm{d} x=10$.
B. $\int\limits_{4}^{8}{f\left( x \right)\text{d}x}=1$.
C. $\int\limits_{4}^{8}{f\left( x \right)\text{d}x}=-5$.
D. $\int_{1}^{4}[4 f(x)-2 g(x)] \mathrm{d} x=-2$
A. $\int_{1}^{4}[f(x)+g(x)] \mathrm{d} x=10$.
B. $\int\limits_{4}^{8}{f\left( x \right)\text{d}x}=1$.
C. $\int\limits_{4}^{8}{f\left( x \right)\text{d}x}=-5$.
D. $\int_{1}^{4}[4 f(x)-2 g(x)] \mathrm{d} x=-2$
Ta có $\int_{4}^{8} f(x) \mathrm{d} x=\int_{4}^{1} f(x) \mathrm{d} x+\int_{1}^{8} f(x) \mathrm{d} x=-\int_{1}^{4} f(x) \mathrm{d} x+\int_{1}^{8} f(x) \mathrm{d} x=-3-2=-5$.
Mặt khác: $\int_{1}^{4}[4 f(x)-2 g(x)] \mathrm{d} x=4 \int_{1}^{4} f(x) d x-2 \int_{1}^{4} g(x) d x=4.3-2.7=-2$.
$
\int_{1}^{4}[f(x)+g(x)] d x=\int_{1}^{4} f(x) d x+\int_{1}^{4} g(x) d x=3+7=10 \text {. }
$
Mặt khác: $\int_{1}^{4}[4 f(x)-2 g(x)] \mathrm{d} x=4 \int_{1}^{4} f(x) d x-2 \int_{1}^{4} g(x) d x=4.3-2.7=-2$.
$
\int_{1}^{4}[f(x)+g(x)] d x=\int_{1}^{4} f(x) d x+\int_{1}^{4} g(x) d x=3+7=10 \text {. }
$
Đáp án B.