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Today's calculation of Integral 738

Source: 2011 Miyagi University of Education entrance exam

July 4, 2011
calculusintegrationtrigonometrycalculus computations

Problem Statement

Answer the following questions:
(1) Find the value of aa for which S=∫−ππ(x−asin⁡3x)2dxS=\int_{-\pi}^{\pi} (x-a\sin 3x)^2dx is minimized, then find the minimum value.
(2) Find the vlues of p, qp,\ q for which T=∫−ππ(sin⁡3x−px−qx2)2dxT=\int_{-\pi}^{\pi} (\sin 3x-px-qx^2)^2dx is minimized, then find the minimum value.
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