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limit of integral

Source: 2017 South Korea USCM P5

August 15, 2020
Integralreal analysislimitcollege contestscalculusintegration

Problem Statement

Evaluate the following limit. lim⁡n→∞n∫0πsin⁡nxdx\lim_{n\to\infty} \sqrt{n} \int_0^\pi \sin^n x dx
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