Ngân hàng bài tập
B
Xét \(\displaystyle\int\limits_0^2x\cdot\mathrm{e}^{x^2}\mathrm{\,d}x\), nếu đặt \(u=x^2\) thì \(\displaystyle\int\limits_0^2x\cdot\mathrm{e}^{x^2}\mathrm{\,d}x\) bằng
 | \(2\displaystyle\int\limits_0^2\mathrm{e}^u\mathrm{\,d}u\) |
 | \(2\displaystyle\int\limits_0^4\mathrm{e}^u\mathrm{\,d}u\) |
 | \(\dfrac{1}{2}\displaystyle\int\limits_0^2\mathrm{e}^u\mathrm{\,d}u\) |
 | \(\dfrac{1}{2}\displaystyle\int\limits_0^4\mathrm{e}^u\mathrm{\,d}u\) |
1 lời giải
Chọn phương án D.
Đặt \(u=x^2\Rightarrow\mathrm{\,d}u=2x\mathrm{\,d}x\).
- \(x=0\Rightarrow u=0\)
- \(x=2\Rightarrow u=4\)
Khi đó \(\displaystyle\int\limits_0^2x\cdot\mathrm{e}^{x^2}\mathrm{\,d}x=\dfrac{1}{2}\displaystyle\int\limits_0^4\mathrm{e}^u\mathrm{\,d}u\).