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Today's calculation of Integral 794

Source: 2012 Tohoku University entrance exam/Science、problem 4

February 27, 2012
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Define a function f(x)=∫0π2cos⁡∣t−x∣1+sin⁡∣t−x∣dtf(x)=\int_0^{\frac{\pi}{2}} \frac{\cos |t-x|}{1+\sin |t-x|}dt for 0≤x≤π0\leq x\leq \pi.
Find the maximum and minimum value of f(x)f(x) in 0≤x≤π0\leq x\leq \pi.
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