মান নির্ণয় করো -- int_1^sqrt3 (dx)/(1+x^2)
Explanation: 
Another Explanation (5):
সমাধান:
আমরা জানি, \( \int \frac{1}{1+x^2} dx = \tan^{-1}(x) + C \)
অতএব,
\[
\begin{aligned}
\int_1^{\sqrt{3}} \frac{dx}{1+x^2} &= \left[ \tan^{-1}(x) \right]_1^{\sqrt{3}} \\
&= \tan^{-1}(\sqrt{3}) - \tan^{-1}(1) \\
&= \frac{\pi}{3} - \frac{\pi}{4} \\
&= \frac{4\pi - 3\pi}{12} \\
&= \frac{\pi}{12}
\end{aligned}
\]
সুতরাং, \(\int_1^{\sqrt{3}} \frac{dx}{1+x^2} = \frac{\pi}{12}\) 🎉
