问题
已知 $\alpha$ 和 $\beta$ 为常数，则 $\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $?$选项
[A]. $\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\alpha$ $\int_{L}$ $\boldsymbol{F}_{1}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $\times$ $\beta$ $\int_{L}$ $\boldsymbol{F}_{2}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$[B]. $\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\alpha$ $\int_{L}$ $\boldsymbol{F}_{1}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $-$ $\beta$ $\int_{L}$ $\boldsymbol{F}_{2}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
[C]. $\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\alpha$ $\int_{L}$ $\boldsymbol{F}_{1}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\beta$ $\int_{L}$ $\boldsymbol{F}_{2}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
[D]. $\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\frac{1}{\alpha}$ $\int_{L}$ $\boldsymbol{F}_{1}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\frac{1}{\beta}$ $\int_{L}$ $\boldsymbol{F}_{2}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$
$\int_{L}$ $\big[$ $\alpha$ $\boldsymbol{F}_{1}(x, y)$ $+$ $\beta$ $\boldsymbol{F}_{2}(x, y)$ $\big]$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $=$ $\alpha$ $\int_{L}$ $\boldsymbol{F}_{1}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$ $+$ $\beta$ $\int_{L}$ $\boldsymbol{F}_{2}(x, y)$ $\cdot$ $\mathrm{d} \boldsymbol{r}$