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Today's calculation of integral 99

Source: 1980 Meiji University entrance exam

March 30, 2006
calculusintegrationtrigonometryreal analysissymmetryfunctioncalculus computations

Problem Statement

Let θ\theta be a constant number such that 0≤θ≤π.0\leq \theta \leq \pi. Evaluate ∫02πsin⁡8x∣sin⁡(x−θ)∣ dx. \int_0^{2\pi} \sin 8x|\sin (x-\theta)|\ dx.
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