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Câu hỏi: Xét $I=\int\limits_{0}^{1}{2x{{\left( {{x}^{2}}+2 \right)}^{2022}}dx}$, nếu đặt $u={{x}^{2}}+2$ thì $I$ bằng
A. $\int\limits_{2}^{3}{{{u}^{2022}}du}$.
B. $\int\limits_{0}^{1}{{{u}^{2022}}du}$.
C. $2\int\limits_{2}^{3}{{{u}^{2022}}du}$.
D. $\dfrac{1}{2}\int\limits_{2}^{3}{{{u}^{2022}}du}$.
Đặt $u={{x}^{2}}+2$. Đổi cận: $x=0\Rightarrow u=2$ ; $x=1\Rightarrow u=3$. Khi đó $I=\int\limits_{2}^{3}{{{u}^{2022}}du}$
A. $\int\limits_{2}^{3}{{{u}^{2022}}du}$.
B. $\int\limits_{0}^{1}{{{u}^{2022}}du}$.
C. $2\int\limits_{2}^{3}{{{u}^{2022}}du}$.
D. $\dfrac{1}{2}\int\limits_{2}^{3}{{{u}^{2022}}du}$.
Xét $I=\int\limits_{0}^{1}{2x{{\left( {{x}^{2}}+2 \right)}^{20202}}dx}=\int\limits_{0}^{1}{{{\left( {{x}^{2}}+2 \right)}^{2022}}d\left( {{x}^{2}}+2 \right)}$ Đặt $u={{x}^{2}}+2$. Đổi cận: $x=0\Rightarrow u=2$ ; $x=1\Rightarrow u=3$. Khi đó $I=\int\limits_{2}^{3}{{{u}^{2022}}du}$
Đáp án A.