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Câu hỏi: Cho hàm số $f\left( x \right)=\left\{ \begin{aligned}
& 2{{x}^{2}}+x\text{ khi }x\ge 0 \\
& x\sin x\text{ khi }x\le 0 \\
\end{aligned} \right. $. Tính $ I=\int\limits_{-\pi }^{1}{f\left( x \right)dx}$.
A. $I=\dfrac{7}{6}+\pi $.
B. $I=\dfrac{2}{3}+\pi $.
C. $I=3\pi -\dfrac{1}{3}$.
D. $I=\dfrac{2}{5}+2\pi $.
& 2{{x}^{2}}+x\text{ khi }x\ge 0 \\
& x\sin x\text{ khi }x\le 0 \\
\end{aligned} \right. $. Tính $ I=\int\limits_{-\pi }^{1}{f\left( x \right)dx}$.
A. $I=\dfrac{7}{6}+\pi $.
B. $I=\dfrac{2}{3}+\pi $.
C. $I=3\pi -\dfrac{1}{3}$.
D. $I=\dfrac{2}{5}+2\pi $.
$I=\int\limits_{-\pi }^{1}{f\left( x \right)dx}=\int\limits_{-\pi }^{0}{f\left( x \right)dx}+\int\limits_{0}^{1}{f\left( x \right)dx}=\int\limits_{-\pi }^{0}{x\sin xdx}+\int\limits_{0}^{1}{\left( 2{{x}^{2}}+x \right)dx}$
$=\left. \left( \sin x-x\cos x \right) \right|_{-\pi }^{0}+\left. \left( \dfrac{2}{3}{{x}^{3}}+\dfrac{1}{2}{{x}^{2}} \right) \right|_{0}^{1}=\dfrac{7}{6}+\pi $.
$=\left. \left( \sin x-x\cos x \right) \right|_{-\pi }^{0}+\left. \left( \dfrac{2}{3}{{x}^{3}}+\dfrac{1}{2}{{x}^{2}} \right) \right|_{0}^{1}=\dfrac{7}{6}+\pi $.
Đáp án A.