Cho

B

- Hướng dẫn giải

Đáp án B

Ta có ${\int }_5^{4}f\left(t\right)dt=-{\int }_5^{4}f\left(t\right)dt=-2\Rightarrow {\int }_5^{4}f\left(t\right)dt={\int }_5^{4}f\left(x\right)dx=2$ .

Suy ra ${\int }_{-1}^{5}f\left(x\right)dx+{\int }_4^{5}f\left(t\right)dt={\int }_{-1}^{5}f\left(x\right)dx+{\int }_5^{4}f\left(x\right)dx={\int }_{-1}^{4}f\left(x\right)dx=7.$ 

Khi đó

${\int }_{-1}^4\left(f\left(x\right)+g\left(x\right)\right)dx+{\int }_{-1}^{4}f\left(x\right)dx+{\int }_{-1}^{4}g\left(x\right)dx={\int }_{-1}^{4}f\left(x\right)dx+{\int }_5^{4}f\left(x\right)dx={\int }_{-1}^{4}g\left(u\right)du=7+\frac{1}{3}=\frac{22}{3}.$