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Mathematics
Problem The function
f ( x ) = ∫ 0 x log ∣ sin t ∣ ( sin t + 1 2 ) d t , where x ∈ ( 0 , 2 π ) , then f(x) = \int_{0}^{x} \log_{|\sin t|} \left( \sin t + \frac{1}{2} \right) dt, \text{ where } x \in (0, 2\pi), \text{ then} f ( x ) = ∫ 0 x log ∣ s i n t ∣ ( sin t + 2 1 ) d t , where x ∈ ( 0 , 2 π ) , then f ( x ) f(x) f ( x ) ( π 6 , 5 π 6 ) \left( \frac{\pi}{6}, \frac{5\pi}{6} \right) ( 6 π , 6 5 π ) ( 5 π 6 , 2 π ) \left( \frac{5\pi}{6}, 2\pi \right) ( 6 5 π , 2 π ) ( π 6 , 7 π 6 ) \left( \frac{\pi}{6}, \frac{7\pi}{6} \right) ( 6 π , 6 7 π ) ( 5 π 6 , 7 π 6 ) \left( \frac{5\pi}{6}, \frac{7\pi}{6} \right) ( 6 5 π , 6 7 π ) Browse the problem library