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Today's calculation of Integral 688

Source:

March 1, 2011
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

For a real number xx, let f(x)=∫0π2∣cos⁡t−xsin⁡2t∣ dtf(x)=\int_0^{\frac{\pi}{2}} |\cos t-x\sin 2t|\ dt.
(1) Find the minimum value of f(x)f(x).
(2) Evaluate ∫01f(x) dx\int_0^1 f(x)\ dx.
2011 Tokyo Institute of Technology entrance exam, Problem 2
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