int_0^1 dx/(1+x^2) এর মান কত?

আমরা জানি, \( \int \frac{1}{1+x^2} dx = \tan^{-1}(x) + C \)।

সুতরাং, \( \int_0^1 \frac{dx}{1+x^2} = \left[ \tan^{-1}(x) \right]_0^1 \)。

এখন, \( \tan^{-1}(1) = \frac{\pi}{4} \) এবং \( \tan^{-1}(0) = 0 \)।

অতএব, \( \int_0^1 \frac{dx}{1+x^2} = \tan^{-1}(1) - \tan^{-1}(0) = \frac{\pi}{4} - 0 = \frac{\pi}{4} \)। 🎉

সুতরাং, \( \int_0^1 \frac{dx}{1+x^2} = \frac{\pi}{4} \)। ✅