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Today's calculation of Integral 312

Source: 2008 Tokyo Metropolitan University entrance exam/Science

March 30, 2008
calculusintegrationfunctionanalytic geometrycalculus computations

Problem Statement

Let a, b a,\ b be postive real numbers. For a real number t t, denote by d(t)d(t) the distance between the origin and the line (ae^t)x \plus{} (be^{ \minus{} t})y \equal{} 1.
Let a, b a,\ b vary with ab \equal{} 1, find the minimum value of ∫011d(t)2 dt \int_0^1 \frac {1}{d(t)^2}\ dt.
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