Đặt \(t=\sqrt{x}\Rightarrow\left\{{}\begin{matrix}x=t^2\\dx=2dt\end{matrix}\right.\)
\(x=0\Rightarrow t=0\)
\(x=\dfrac{\pi^2}{4}\Rightarrow t=\dfrac{\pi}{2}\)
\(\Rightarrow I=2\int\limits^{\dfrac{\pi}{2}}_0tcos\left(t\right)dt\)
Đặt \(u=t;dv=costdt\Rightarrow du=dt;v=sint\)
\(\Rightarrow\int udv=uv-\int vdu\) (Tích phân từng phần)
\(\Rightarrow I=2\left[tsint|^{\dfrac{\pi}{2}}_0-\int\limits^{\dfrac{\pi}{2}}_0sintdt\right]\)
\(\Rightarrow I=2\left[\dfrac{\pi}{2}.sin\dfrac{\pi}{2}-0.sin0+cost|^{\dfrac{\pi}{2}}_0\right]=2\left[\dfrac{\pi}{2}-0-1\right]=\pi-2\)
Đúng 2
Bình luận (0)
