MathDB

738

Part of 2011 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 738

Source: 2011 Miyagi University of Education entrance exam

7/4/2011
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.
calculusintegrationtrigonometrycalculus computations