Cho biết

12/40

Cho biết \[\mathop \smallint \limits_1^3 f\left( x \right)dx = - 2,\mathop \smallint \limits_1^4 f\left( x \right)dx = 3,\mathop \smallint \limits_1^4 g\left( x \right)dx = 7\]. Chọn khẳng định sai?

\[\mathop \smallint \limits_1^4 \left[ {f\left( x \right) + g\left( x \right)} \right]dx = 10\]

\[\mathop \smallint \limits_3^4 f\left( x \right)dx = - 5\]

\[\mathop \smallint \limits_3^4 f\left( x \right)dx = 5\]

\[\mathop \smallint \limits_1^4 \left[ {4f\left( x \right) - 2g\left( x \right)} \right]dx = - 2\]

Giải thích

Ta có:\[\mathop \smallint \limits_1^4 \left[ {f\left( x \right) + g\left( x \right)} \right]dx = \mathop \smallint \limits_1^4 f\left( x \right)dx + \mathop \smallint \limits_1^4 f\left( x \right)dx = 10\] nên A đúng.

\[\mathop \smallint \limits_1^4 f\left( x \right)dx = \mathop \smallint \limits_1^3 f\left( x \right)dx + \mathop \smallint \limits_3^4 f\left( x \right)dx \Rightarrow \mathop \smallint \limits_3^4 f\left( x \right)dx = \mathop \smallint \limits_1^4 f\left( x \right)dx - \mathop \smallint \limits_1^3 f\left( x \right)dx = 3 - \left( { - 2} \right) = 5\]nên C đúng, B sai.

\[\mathop \smallint \limits_1^4 \left[ {4f\left( x \right) - 2g\left( x \right)} \right]dx = 4\mathop \smallint \limits_1^4 f\left( x \right)dx - 2\mathop \smallint \limits_1^4 g\left( x \right)dx = - 2\]nên D đúng.

Đáp án cần chọn là: B