Google
Câu hỏi: Biết $F\left( x \right)$ là một nguyên hàm của $f\left( x \right)$ và $\int{F\left( x \right)\text{d}x}={{x}^{2022}}+C$. Chọn khẳng định đúng.
A. $\int{xf\left( x \right)\text{d}x}=xF\left( x \right)+{{x}^{2022}}+C.$
B. $\int{xf\left( x \right)\text{d}x}=xF\left( x \right)-{{x}^{2022}}-C.$
C. $\int{xf\left( x \right)\text{d}x}=xf\left( x \right)-{{x}^{2022}}-C.$
D. $\int{xf\left( x \right)\text{d}x}=xf\left( x \right)+2022{{x}^{2021}}+C.$
A. $\int{xf\left( x \right)\text{d}x}=xF\left( x \right)+{{x}^{2022}}+C.$
B. $\int{xf\left( x \right)\text{d}x}=xF\left( x \right)-{{x}^{2022}}-C.$
C. $\int{xf\left( x \right)\text{d}x}=xf\left( x \right)-{{x}^{2022}}-C.$
D. $\int{xf\left( x \right)\text{d}x}=xf\left( x \right)+2022{{x}^{2021}}+C.$
Đặt $\left\{ \begin{aligned}
& u=x \\
& \text{d}v=f\left( x \right)\text{d}x \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& \text{d}u=\text{d}x \\
& v=F\left( x \right) \\
\end{aligned} \right.$
$\Rightarrow \int{xf\left( x \right)dx}=xF\left( x \right)-\int{F\left( x \right)\text{d}x}=xF\left( x \right)-{{x}^{2022}}-C$.
& u=x \\
& \text{d}v=f\left( x \right)\text{d}x \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& \text{d}u=\text{d}x \\
& v=F\left( x \right) \\
\end{aligned} \right.$
$\Rightarrow \int{xf\left( x \right)dx}=xF\left( x \right)-\int{F\left( x \right)\text{d}x}=xF\left( x \right)-{{x}^{2022}}-C$.
Đáp án B.