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Today's calculation of Integral 458

Source: 2009 Shimane University entrance exam

June 27, 2009
calculusintegrationgeometrylogarithmsvectorcalculus computations

Problem Statement

Let S(t) S(t) be the area of the traingle OAB OAB with O(0,\ 0,\ 0),\ A(2,\ 2,\ 1),\ B(t,\ 1,\ 1 \plus{} t). Evaluate ∫1eS(t)2ln⁡t dt \int_1^ e S(t)^2\ln t\ dt.
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