int_0^(π/2) sin^5 theta costheta d theta মান হবে -

Explanation:

Another Explanation (5): সমাধান: ধরি, \( sin \theta = z \) তাহলে, \( cos \theta d\theta = dz \) যখন \( \theta = 0 \), তখন \( z = sin(0) = 0 \) যখন \( \theta = \frac{\pi}{2} \), তখন \( z = sin(\frac{\pi}{2}) = 1 \) সুতরাং, \( \int_{0}^{\frac{\pi}{2}} sin^5 \theta cos \theta d\theta = \int_{0}^{1} z^5 dz \) \( = [\frac{z^6}{6}]_{0}^{1} \) \( = \frac{1^6}{6} - \frac{0^6}{6} \) \( = \frac{1}{6} - 0 \) \( = \frac{1}{6} \) অতএব, \( \int_{0}^{\frac{\pi}{2}} sin^5 \theta cos \theta d\theta = \frac{1}{6} \) 🥳