a.
Đặt \(\left\{{}\begin{matrix}u=2-x\\dv=sinxdx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=-dx\\v=-cosx\end{matrix}\right.\)
\(\Rightarrow I=\left(x-2\right).cosx|^{\dfrac{\pi}{2}}_0-\int\limits^{\dfrac{\pi}{2}}_0cosx.dx=2-1=1\)
b. Đặt \(cos2x=t\Rightarrow-2sin2x.dx=dt\Rightarrow sin2xdx=-\dfrac{1}{2}dt\)
\(\left\{{}\begin{matrix}x=0\Rightarrow t=1\\x=\pi\Rightarrow t=1\end{matrix}\right.\)
\(\Rightarrow I=\int\limits^1_1-\dfrac{1}{2}.t^2dt=0\) (hai cận bằng nhau thì tích phân bằng 0 khỏi tính dài dòng)
c. Đặt \(\left\{{}\begin{matrix}u=x\\dv=e^xdx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=dx\\v=e^x\end{matrix}\right.\)
\(I=x.e^x|^1_0-\int\limits^1_0e^xdx=\left(x.e^x-e^x\right)|^1_0=1\)
