My First Nameless Problem

Calculus Level pending

\[I=\lim_{n\to \infty} \displaystyle \frac{1}{n^{n+1}} \int_{0}^{n} x^n\cdot \sin x dx+\lim_{n\to 0}\frac{1}{n^{n+1}}\int_{0}^{n}x^n\cdot \sin x dx\]

Let \(n=4p\) such that \(p\) is a positive integer satisfying the equation above.

Find the value of \(I\)

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