Nếu \(\int\limits_{2}^{9}{f(x)}dx=8\) ; \(\int\limits_{5}^{13}{f(x)}dx=10\) và \(\int\limits_{5}^{9}{f(x)}dx=6\).Tính \(\int_{2}^{13}{f}(x)\text{d}x\)

* Hướng dẫn giải

Ta có: \(\int\limits_{2}^{9}{f(x)}dx=\int\limits_{2}^{5}{f(x)}dx+\int\limits_{5}^{9}{f(x)}dx\Leftrightarrow 8=\int\limits_{2}^{5}{f(x)}dx+6\Rightarrow \int\limits_{2}^{5}{f(x)}dx=2\).

Lại có: \(\int\limits_{2}^{13}{f(x)}dx=\int\limits_{2}^{5}{f(x)}dx+\int\limits_{5}^{13}{f(x)}dx=2+10=12\).