Evaluate

Chapter 14, Problem 73

(choose chapter or problem)

Evaluate

\(\lim _{n \rightarrow \infty} \int_{0}^{1} \int_{0}^{1} \cdots \int_{0}^{1} \cos ^{2}\left\{\frac{\pi}{2 n}\left(x_{1}+x_{2}+\cdots+x_{n}\right)\right\} d x_{1} d x_{2} \cdots d x_{n}\).

Text Transcription:

lim _{n rightarrow infty} int_{0}^{1} int_{0}^{1} cdots int_{0}^{1} cos^2 {pi / 2 n} (x_1 + x_2 + cdots + x_n)} dx_1 dx_2 cdots dx_n

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