MathDB
Today's calculation of Integral 64

Source: 1991 Waseda University

July 8, 2005
calculusintegrationalgebrapolynomialtrigonometrycalculus computations

Problem Statement

Let f(t)f(t) be the cubic polynomial for tt such that cos⁡3x=f(cos⁡x)\cos 3x=f(\cos x) holds for all real number xx. Evaluate ∫01{f(t)}21−t2dt\int_0^1 \{f(t)\}^2 \sqrt{1-t^2}dt
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