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Today's calculation of Integral 846

Source: 2012 Saitama University entrance exam/Engineering

September 12, 2012
calculusintegrationlimitlogarithmsfunctionabsolute valuecalculus computations

Problem Statement

For a>0a>0, let f(a)=\lim_{t\to\+0} \int_{t}^1 |ax+x\ln x|\ dx. Let aa vary in the range 0<a<+āˆž0 <a< +\infty, find the minimum value of f(a)f(a).
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