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, \(\int_1^{\sqrt{3}} \frac{dx}{1+x^2} = \frac{\pi}{12}\) 🎉