Cho hàm số f(x) liên tục trên R thỏa mãn \[\mathop \smallint \limits_a^d f\left( x \right)dx = 10,\mathop \smallint \limits_b^d f\left( x \right)dx = 18,\mathop \smallint \limits_a^c f\left( x \right)dx = 7\]. Giá trị của \[\mathop \smallint \limits_b^c f\left( x \right)dx\] là:

Ta có:

\[\begin{array}{*{20}{l}}{\mathop \smallint \limits_a^d f\left( x \right)dx = \mathop \smallint \limits_a^c f\left( x \right)dx + \mathop \smallint \limits_c^b f\left( x \right)dx + \mathop \smallint \limits_b^d f\left( x \right)dx}\\{ \Rightarrow \mathop \smallint \limits_c^b f\left( x \right)dx = \mathop \smallint \limits_a^d f\left( x \right)dx - \mathop \smallint \limits_a^c f\left( x \right)dx - \mathop \smallint \limits_b^d f\left( x \right)dx}\\{ \Rightarrow \mathop \smallint \limits_c^b f\left( x \right)dx = 10 - 7 - 18 = - 15 \Rightarrow \mathop \smallint \limits_b^c f\left( x \right)dx = 15}\end{array}\]

Đáp án cần chọn là: C