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Today's calculation of Integral 281

Source: 1983 Ritsumeikan University entrance exam

January 23, 2008
calculusintegrationtrigonometrycalculus computations

Problem Statement

Find the maximum and minimum values of \int_0^{\pi} (a\sin x\plus{}b\cos x)^3dx for ∣a∣≤1, ∣b∣≤1. |a|\leq 1,\ |b|\leq 1.
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