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Câu hỏi: Cho hàm số $y=f\left( x \right)$ liên tục trên $\left[ 1; 4 \right]$ và thỏa mãn $\int_{1}^{2}{f\left( x \right)dx=\dfrac{1}{2}}$, $\int_{3}^{4}{f\left( x \right)dx=\dfrac{3}{4}}$. Tính giá trị biểu thức $I=\int_{1}^{4}{f\left( x \right)dx-}\int_{2}^{3}{f\left( x \right)dx}$.
A. $I=\dfrac{3}{8}$.
B. $I=\dfrac{5}{4}$.
C. $I=\dfrac{5}{8}$.
D. $I=\dfrac{1}{4}$.
Ta có $I=\int_{1}^{4}{f\left( x \right)dx-}\int_{2}^{3}{f\left( x \right)dx}$ $=\int_{1}^{2}{f\left( x \right)dx+}\int_{2}^{3}{f\left( x \right)dx+\int_{3}^{4}{f\left( x \right)dx}}-\int_{2}^{3}{f\left( x \right)dx}$ $=\int_{1}^{2}{f\left( x \right)dx+}\int_{3}^{4}{f\left( x \right)dx}=$ $\dfrac{1}{2}+\dfrac{3}{4}$ $=\dfrac{5}{4}$.
A. $I=\dfrac{3}{8}$.
B. $I=\dfrac{5}{4}$.
C. $I=\dfrac{5}{8}$.
D. $I=\dfrac{1}{4}$.
Ta có $I=\int_{1}^{4}{f\left( x \right)dx-}\int_{2}^{3}{f\left( x \right)dx}$ $=\int_{1}^{2}{f\left( x \right)dx+}\int_{2}^{3}{f\left( x \right)dx+\int_{3}^{4}{f\left( x \right)dx}}-\int_{2}^{3}{f\left( x \right)dx}$ $=\int_{1}^{2}{f\left( x \right)dx+}\int_{3}^{4}{f\left( x \right)dx}=$ $\dfrac{1}{2}+\dfrac{3}{4}$ $=\dfrac{5}{4}$.
Đáp án B.