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74

Part of 2005 Today's Calculation Of Integral

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Today's Calculation of Integral 74

Source: 1978 Nagoya University

7/22/2005
p,qp,q satisfies px+q≥ln⁡xpx+q\geq \ln x at a≤x≤b (0<a<b)a\leq x\leq b\ (0<a<b). Find the value of p,qp,q for which the following definite integral is minimized and then the minimum value. ∫ab(px+q−ln⁡x)dx\int_a^b (px+q-\ln x)dx
calculusintegrationlogarithmscalculus computations