Đáp án:
\(I = - 1 - \dfrac{3\pi}{4}\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad I = \displaystyle\int\limits_{\tfrac{\pi}{2}}^{\tfrac{\pi}{4}}\left(4 + \cot^2t\right)dt\\
\to I = \displaystyle\int\limits_{\tfrac{\pi}{2}}^{\tfrac{\pi}{4}}\left(3 + \dfrac{1}{\sin^2t}\right)dt\\
\to I = \left(3t - \cot t\right)\Bigg|_{\tfrac{\pi}{2}}^{\tfrac{\pi}{4}}\\
\to I = - 1 - \dfrac{3\pi}{4}
\end{array}\)
