Google
Câu hỏi: Cho tích phân $I=\int\limits_{0}^{\dfrac{\pi }{4}}{x{{e}^{x}}dx}$. Tìm đẳng thức đúng?
A. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}+\int\limits_{0}^{1}{{{e}^{x}}dx}$.
B. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. {{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
C. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
D. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{xdx}$.
A. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}+\int\limits_{0}^{1}{{{e}^{x}}dx}$.
B. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. {{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
C. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
D. $I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{xdx}$.
Đặt $\left\{ \begin{aligned}
& u=x \\
& dv={{e}^{x}}dx \\
\end{aligned} \right. $. Ta có $ \left\{ \begin{aligned}
& du=dx \\
& v={{e}^{x}} \\
\end{aligned} \right. $. Do đó $ I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
& u=x \\
& dv={{e}^{x}}dx \\
\end{aligned} \right. $. Ta có $ \left\{ \begin{aligned}
& du=dx \\
& v={{e}^{x}} \\
\end{aligned} \right. $. Do đó $ I=\int\limits_{0}^{1}{x{{e}^{x}}dx}=\left. x{{e}^{x}} \right|_{0}^{1}-\int\limits_{0}^{1}{{{e}^{x}}dx}$.
Đáp án C.