A question asked by Sourav De and Shafiqur Rahman

Evaluate $ \lim_{n \to \infty}n \int_0^{\frac{\pi}{2}} (1 - \sqrt[n]{\sin x}) \; dx $

Related one originally posted by Shafiqur Rahman as below:

Evaluate $ \lim_{n \to \infty}n \int_0^{\frac{\pi}{2}} (1 - \sqrt[3n]{\sin x}) \; dx $

Answer: will be available soon.