Ngân hàng bài tập
A
Nếu $\displaystyle\displaystyle\int\limits_1^3f(x)\mathrm{\,d}x=3$ thì $\displaystyle\displaystyle\int\limits_1^5f\left(\dfrac{x+1}{2}\right)\mathrm{\,d}x$ bằng
 | $\dfrac{3}{2}$ |
 | $3$ |
 | $\dfrac{5}{2}$ |
 | $6$ |
1 lời giải
Chọn phương án D.
Đặt $u=\dfrac{x+1}{2}\Rightarrow\mathrm{d}u=\dfrac{1}{2}\mathrm{d}x$ hay $\mathrm{d}x=2\mathrm{d}u$.
- $x=1\Rightarrow u=1$
- $x=5\Rightarrow u=3$
$\begin{aligned}\Rightarrow\displaystyle\int\limits_1^5f\left(\dfrac{x+1}{2}\right)\mathrm{\,d}x&=\displaystyle\int\limits_1^3f(u)\cdot2\mathrm{\,d}u\\ &=2\displaystyle\int\limits_1^3f(x)\mathrm{\,d}x=2\cdot3=6.\end{aligned}$