int 2sin^2 (x/2) dx=  কত?

Explanation:

Another Explanation (5): সমাধান: আমরা জানি, \( \sin^2 \theta = \frac{1 - \cos 2\theta}{2} \) সুতরাং, \( \sin^2 \frac{x}{2} = \frac{1 - \cos x}{2} \) অতএব, \( \int 2\sin^2 \frac{x}{2} \, dx = \int 2 \cdot \frac{1 - \cos x}{2} \, dx \) \( = \int (1 - \cos x) \, dx \) \( = \int 1 \, dx - \int \cos x \, dx \) \( = x - \sin x + c \) 🥳 সুতরাং, \( \int 2\sin^2 \frac{x}{2} \, dx = x - \sin x + c \) 😎 উত্তর: \( x - \sin x + c \) 🎉