Cho hàm số $f(x)$ liên tục trên $\mathbb{R}$ thỏa $\displaystyle\displaystyle\int\limits_{0}^{6}f(x)\mathrm{\,d}x=7$, $\displaystyle\displaystyle\int\limits_{3}^{10}f(x)\mathrm{\,d}x=8$, $\displaystyle\displaystyle\int\limits_{3}^{6}f(x)\mathrm{\,d}x=9$. Giá trị của $I=\displaystyle\displaystyle\int\limits_{0}^{10}f(x)\mathrm{\,d}x$ bằng
 | $8$ |
 | $6$ |
 | $7$ |
 | $5$ |
Chọn phương án B.
Ta có $\displaystyle\int\limits_{3}^{10}f(x)\mathrm{\,d}x=\displaystyle\int\limits_{3}^{6}f(x)\mathrm{\,d}x+\displaystyle\int\limits_{6}^{10}f(x)\mathrm{\,d}x$.
Suy ra $\displaystyle\int\limits_{6}^{10}f(x)\mathrm{\,d}x=\displaystyle\int\limits_{3}^{10}f(x)\mathrm{\,d}x-\displaystyle\int\limits_{3}^{6}f(x)\mathrm{\,d}x=8-9=-1$.
Khi đó $I=\displaystyle\int\limits_{0}^{10}f(x)\mathrm{\,d}x=\displaystyle\int\limits_{0}^{6}f(x)\mathrm{\,d}x+\displaystyle\int\limits_{6}^{10}f(x)\mathrm{\,d}x=7-1=6$.