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85

Part of 2005 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 85

Source: 1991 Ochanomizu Women University Entrance exam

9/27/2005
Evaluate lim⁡n→∞∫0π2[nsin⁡x]n dx\lim_{n\to\infty} \int_0^{\frac{\pi}{2}} \frac{[n\sin x]}{n}\ dx where [x] [x] is the integer equal to x x or less than x x .
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