Nếu \(\int\limits_a^d {f(x)\,dx = 5\,,\,\,\int\lim...

A

- Hướng dẫn giải

Ta có:

$\left\{ \begin{array}{l}\int\limits_a^d {f\left( x \right)dx = 5\,} \\\int\limits_b^d {f\left( x \right)\,dx = 2} \,\end{array} \right. \\\Rightarrow \left\{ \begin{array}{l}\int\limits_a^d {f\left( x \right)dx = 5\,} \\ - \int\limits_d^b {f\left( x \right)\,dx = 2} \,\end{array} \right. \\\Leftrightarrow \left\{ \begin{array}{l}\int\limits_a^d {f\left( x \right)dx = 5\,} \\\int\limits_d^b {f\left( x \right)\,dx =  - 2} \,\end{array} \right.$

Khi đó ta có: $\int\limits_a^d {f\left( x \right)dx\, + \int\limits_d^b {f\left( x \right)\,dx} \,}$$\,= 5 + \left( { - 2} \right) = 3.$