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Today's calculation of Integral 622

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July 1, 2010
calculusintegrationtrigonometrygeometryanalytic geometryfunctioncalculus computations

Problem Statement

For 0<k<20<k<2, consider two curves C1:y=sin⁡2x (0≤x≤π), C2:y=kcos⁡x (0≦x≦π).C_1: y=\sin 2x\ (0\leq x\leq \pi),\ C_2: y=k\cos x\ (0\leqq x\leqq \pi). Denote by S(k)S(k) the sum of the areas of four parts enclosed by C1, C2C_1,\ C_2 and two lines x=0, x=πx=0,\ x=\pi. Find the minimum value of S(k).S(k).
2010 Nagoya Institute of Technology entrance exam
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