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Show that a particularly easy primitivable function is irrational

Source: Romanian District Olympiad 2011, Grade XII, Problem 1

October 8, 2018
functionIntegralprimitivesFTCcalculus

Problem Statement

Prove the rationality of the number 1π∫sin⁡π13cos⁡π131−x2dx. \frac{1}{\pi }\int_{\sin\frac{\pi }{13}}^{\cos\frac{\pi }{13}} \sqrt{1-x^2} dx.
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