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Today's calculation of Integral 81

Source: 1978 Kyoto Institute of Technology Entrance Exam

September 8, 2005
calculusintegrationlogarithmstrigonometryinequalitiesderivativefunction

Problem Statement

Prove the following inequality. 112(π−6+23)≤∫π6π4ln⁡(1+cos⁡2x)dx≤14(2−3)\frac{1}{12}(\pi -6+2\sqrt{3})\leq \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \ln (1+\cos 2x) dx\leq \frac{1}{4}(2-\sqrt{3})
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