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Câu hỏi: Xét $\int\limits_{0}^{2}{{{\left( 1-\dfrac{x}{2} \right)}^{20}}\text{d}x}$ nếu đặt $u=1-\dfrac{x}{2}$ thì $\int\limits_{0}^{2}{{{\left( 1-\dfrac{x}{2} \right)}^{20}}\text{d}x}$ bằng
A. $\dfrac{1}{2}\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
B. $-\dfrac{1}{2}\int\limits_{-1}^{1}{{{u}^{20}}\text{d}u}$.
C. $\int\limits_{-1}^{1}{{{u}^{20}}\text{d}u}$.
D. $2\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
A. $\dfrac{1}{2}\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
B. $-\dfrac{1}{2}\int\limits_{-1}^{1}{{{u}^{20}}\text{d}u}$.
C. $\int\limits_{-1}^{1}{{{u}^{20}}\text{d}u}$.
D. $2\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
Đặt $u=1-\dfrac{x}{2}$ $\Rightarrow \text{d}u=-\dfrac{1}{2}\text{d}x$ $\Rightarrow \text{d}x=-2\text{d}u$.
Đổi cận: $x=0\Rightarrow u=1$, $x=2\Rightarrow u=0$.
$\Rightarrow \int\limits_{0}^{2}{{{\left( 1-\dfrac{x}{2} \right)}^{20}}\text{d}x}$ $=-2\int\limits_{1}^{0}{{{u}^{20}}\text{d}u}$ $=2\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
Đổi cận: $x=0\Rightarrow u=1$, $x=2\Rightarrow u=0$.
$\Rightarrow \int\limits_{0}^{2}{{{\left( 1-\dfrac{x}{2} \right)}^{20}}\text{d}x}$ $=-2\int\limits_{1}^{0}{{{u}^{20}}\text{d}u}$ $=2\int\limits_{0}^{1}{{{u}^{20}}\text{d}u}$.
Đáp án D.