Google
Câu hỏi: Biết $\int\limits_{1}^{3}{f\left( x \right)\text{d}x=4; }\int\limits_{1}^{3}{g\left( x \right)\text{d}x=-2}$. Tính $\int\limits_{1}^{3}{2\left[ g\left( x \right)-f\left( x \right) \right]}\text{d}x$
A. $-6$.
B. $-12$.
C. $6$.
D. $12$.
A. $-6$.
B. $-12$.
C. $6$.
D. $12$.
Ta có
$\int\limits_{1}^{3}{2\left[ g\left( x \right)-f\left( x \right) \right]}\text{d}x=2\int\limits_{1}^{3}{\left[ g\left( x \right)-f\left( x \right) \right]}\text{d}x=2\left[ \int\limits_{1}^{3}{g\left( x \right)}\text{d}x-\int\limits_{1}^{3}{f\left( x \right)}\text{d}x \right]=2\left( -2-4 \right)=-12$.
$\int\limits_{1}^{3}{2\left[ g\left( x \right)-f\left( x \right) \right]}\text{d}x=2\int\limits_{1}^{3}{\left[ g\left( x \right)-f\left( x \right) \right]}\text{d}x=2\left[ \int\limits_{1}^{3}{g\left( x \right)}\text{d}x-\int\limits_{1}^{3}{f\left( x \right)}\text{d}x \right]=2\left( -2-4 \right)=-12$.
Đáp án B.