Yes Ricky you are saying right.
\mathbf{\lim_{n\to\infty}n.\int_{0}^{\frac{\pi}{2}}\left(1-\sqrt[n]{sinx}\right)dx=}$\\\\ \textbf{Ans::\Rightarrow \mathbf{\displaystyle \frac{\pi.ln(2)}{2}}}
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\mathbf{\lim_{n\to\infty}n.\int_{0}^{\frac{\pi}{2}}\left(1-\sqrt[n]{sinx}\right)dx=}$\\\\ \textbf{Ans::\Rightarrow \mathbf{\displaystyle \frac{\pi.ln(2)}{2}}}