Ngân hàng bài tập
B
Nếu đặt $u=2x+1$ thì $\displaystyle\displaystyle\int\limits_{0}^{1}(2x+1)^4\mathrm{\,d}x$ bằng
 | $\dfrac{1}{2}\displaystyle\displaystyle\int\limits_{1}^{3}u^4\mathrm{\,d}u$ |
 | $\displaystyle\displaystyle\int\limits_{1}^{3}u^4\mathrm{\,d}u$ |
 | $\dfrac{1}{2}\displaystyle\displaystyle\int\limits_{0}^{1}u^4\mathrm{\,d}u$ |
 | $\displaystyle\displaystyle\int\limits_{0}^{1}u^4\mathrm{\,d}u$ |
1 lời giải
Chọn phương án A.
Với $u=2x+1$ ta có
- $\mathrm{d}u=2\mathrm{d}x$ hay $\mathrm{d}x=\dfrac{1}{2}\mathrm{d}u$.
- $x=0\Rightarrow u=1$
- $x=1\Rightarrow u=3$
Vậy $\displaystyle\int\limits_{0}^{1}(2x+1)^4\mathrm{\,d}x=\dfrac{1}{2}\displaystyle\int\limits_{1}^{3}u^4\mathrm{\,d}u$.