2. Evaluate the following integrals by using reduction formula: a) \( \int_{0}^{\pi} \sin ^{5}\left(\frac{x}{2}\right) d x \) b) \( \int_{0}^{\pi / 6} \operatorname{Sin}^{3}(6 \theta) \operatorname{Cos}^{4}(3 \theta) d \theta \) c) \( \int_{0}^{\pi} \frac{\operatorname{Sin}^{4} x}{(1+\operatorname{Cos} x)^{2}} d x \) e) \( \int_{0}^{\pi} x \operatorname{Sin}^{8}(x) \operatorname{Cos}^{6}(x) d x \quad \) f) \( \int_{0}^{1} x^{2}\left(1-x^{2}\right)^{3 / 2} d x \) g) \( \int_{0}^{\pi / 4} \operatorname{Cos}^{6}(2 t) d t \)

Question

evaluate 1.xsin⁸(x)cos⁶(x)dx using reduction formula 

2.sin³(6theta)cos⁴(3theta)dtheta