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Câu hỏi: Cho $f\left( x \right),g\left( x \right)$ là các hàm liên tục trên $\mathbb{R}.$ Chọn khẳng định sai trong các khẳng định sau đây.
A. $\int\limits_{a}^{b}{f\left( x \right).g\left( x \right)}dx=\int\limits_{a}^{b}{f\left( x \right)dx}.\int\limits_{a}^{b}{g\left( x \right)dx}.$
B. $\int\limits_{a}^{b}{\left[ f\left( x \right)+g\left( x \right) \right]}dx=\int\limits_{a}^{b}{f\left( x \right)dx}+\int\limits_{a}^{b}{g\left( x \right)dx}.$
C. $\int\limits_{a}^{b}{f\left( x \right)dx}=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{b}{f\left( x \right)dx}\text{ }\left( a<c<b \right).$
D. $\int\limits_{a}^{b}{\left[ f\left( x \right)-g\left( x \right) \right]}dx=\int\limits_{a}^{b}{f\left( x \right)dx}-\int\limits_{a}^{b}{g\left( x \right)dx}.$
A. $\int\limits_{a}^{b}{f\left( x \right).g\left( x \right)}dx=\int\limits_{a}^{b}{f\left( x \right)dx}.\int\limits_{a}^{b}{g\left( x \right)dx}.$
B. $\int\limits_{a}^{b}{\left[ f\left( x \right)+g\left( x \right) \right]}dx=\int\limits_{a}^{b}{f\left( x \right)dx}+\int\limits_{a}^{b}{g\left( x \right)dx}.$
C. $\int\limits_{a}^{b}{f\left( x \right)dx}=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{b}{f\left( x \right)dx}\text{ }\left( a<c<b \right).$
D. $\int\limits_{a}^{b}{\left[ f\left( x \right)-g\left( x \right) \right]}dx=\int\limits_{a}^{b}{f\left( x \right)dx}-\int\limits_{a}^{b}{g\left( x \right)dx}.$
Ta có ngay A sai (câu lí thuyết).
Đáp án A.