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Câu hỏi: Cho hàm số $f(x)=\left\{\begin{array}{l}x^2, x \geq 1 \\ x, x<1\end{array}\right.$. Tích phân $\int_0^2 f(x) \mathrm{d} x$ bằng
A. 3 .
B. $\dfrac{17}{6}$.
C. $\dfrac{5}{2}$.
D. $\dfrac{5}{3}$.
A. 3 .
B. $\dfrac{17}{6}$.
C. $\dfrac{5}{2}$.
D. $\dfrac{5}{3}$.
Ta có $\int_0^2 f(x) \mathrm{d} x=\int_0^1 f(x) \mathrm{d} x+\int_1^2 f(x) \mathrm{d} x=\int_0^1 x \mathrm{~d} x+\int_1^2 x^2 \mathrm{~d} x$ $=\left.\left(\dfrac{x^2}{2}\right)\right|_0 ^1+\left.\left(\dfrac{x^3}{3}\right)\right|_1 ^2=\dfrac{1}{2}+\dfrac{8}{3}-\dfrac{1}{3}=\dfrac{17}{6}$
Đáp án B.